Nanostructured titanium-based materials for medical implants: [629669]

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Nanostructured titanium-based materials for medical implants: [629669]

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Nanostructured titanium-based materials for medical implants:
Modeling and development
Leon Mishnaevsky Jr.a,*, Evgeny Levashovb, Ruslan Z. Valievc, Javier Seguradod,
Ilchat Sabirovd, Nariman Enikeevc, Sergey Prokoshkinb, Andrey V. Solov’yove,
Andrey Korotitskiyb, Elazar Gutmanasf, Irene Gotmanf, Eugen Rabkinf, Sergey Psakh’eg,h,
Ludeˇk Dluhos ˇi, Marc Seefeldtj, Alexey Smoling,h
aTechnical University of Denmark, Department of Wind Energy, Risø Campus, Frederiksborgvej 399, DK-4000 Roskilde, Denmark
bNational University of Science and Technology ‘‘MISIS’’, Moscow 119049, Russia
cInstitute of Physics of Advanced Materials, Ufa State Aviation Technical University (IPAM USATU), Ufa 450000, Russia
dIMDEA Materials Institute, Calle Eric Kandel 2, Getafe, 28906 Madrid, Spain
eFIAS, Goethe-Universitaet Frankfurt, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany
fTechnion, Department of Materials Engineering, Technion City, Haifa 32000, Israel
gInstitute of Strength Physics and Materials Science of the Siberian Branch of the Russian Academy of Sciences (ISPMS SB RAS), Tomsk 634050, Russia
hTomsk State University (TSU), Tomsk 634050, Russia
iTimplant Ltd., Sjednocenı ´77/1, CZ72525 Ostrava, Czech Republic
jKU Leuven, Departement MTM, Kasteelpark Arenberg 44, B-3001 Heverlee, Leuven, Belgium
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Titanium as a material of choice for medical implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Nanostructuring of titanium and Ti alloys: concept and technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1. Nanostructuring of titanium and Ti alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2. Severe plastic deformation: processing routes and microstructure evolution. Multiscale computational modeling . . . . . . . . . . . . . . . . 4
3.3. Novel thermomechanical ECAP processing route for fabrication of nano-Ti with very homogeneous structure and superior properties . . . 5
3.4. Thermomechanical treatment of UFG Ti–Ni alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Materials Science and Engineering R 81 (2014) 1–19
A R T I C L E I N F O
Article history:
Available online 22 May 2014
Guiding Editor: Franky So
Keywords:Ultraﬁne grained titanium
Medical implants
Computational modeling
Severe plastic deformation
Thermomechanical processing
NitinolA B S T R A C T
Nanostructuring of titanium-based implantable devices can provide them with superior mechanical
properties and enhanced biocompatibity. An overview of advanced fabrication technologies of
nanostructured, high strength, biocompatible Ti and shape memory Ni–Ti alloy for medical implants is
given. Computational methods of nanostructure properties simulation and various approaches to the
computational, ‘‘virtual’’ testing and numerical optimization of these materials are discussed. Applications
of atomistic methods, continuum micromechanics and crystal plasticity as well as analytical models to the
analysis of the reserves of the improvement of materials for medical implants are demonstrated. Examples
of successful development of a nanomaterial-based medical implants are presented.
/C223 2014 Elsevier B.V. All rights reserved.
Abbreviations: ABAQUS, commercial ﬁnite element software; ARB, accumulative roll bonding; CP, crystal plasticity; DFT, density functional theory; ECAP, equal channel
angular pressing; ECAP-C, equal channel angular pressing – conform; FE, ﬁnite elements; GB, grain boundary; HE, hydrostatic extrusion; HPT, high pressure torsion; GGA,
generalized gradient approximation; LDA, local density approximation; MCA, movable cellular automata; MD, molecular dynamics; MLPs, martensite lattice parameters;
MTLS MAX, maximum martensitic transformation; MUBINAF, multicomponent bioactive nanostructured ﬁlms; NEGB, non-equilibrium grain boundary; PDA, post-
deformation annealing; RSEM-RVE, representative volume element (micromechanics of materials); PIRAC, powder immersion reaction assisted coating; RRSPC, lattice strain
resource recoverable strain; SEM, scanning electron microscopy; SPM, scanning probe microscopy; SPD, severe plastic deformation; TEM, transmission electron microscopy;
UFG, ultra ﬁne grained; UMAT,VUMAT, ABAQUS user subroutines; VPSC, visco-plastic self-consistent model; TJR, total joint replacements; XRD, X ray diffraction.
*Corresponding author.
E-mail address: lemi@dtu.dk (L. Mishnaevsky Jr.).Contents lists available at ScienceDirect
Materials Science and Engineering R
jou r nal h o mep ag e: w ww .elsevier .co m /loc ate/m ser
http://dx.doi.org/10.1016/j.mser.2014.04.0020927-796X/ /C223 2014 Elsevier B.V. All rights reserved.

3.5. Comparison of cold sintering and ECAP processing routes of nanostructuring Ti-based materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4. Superior mechanical properties of UFG titanium-based materials: computational modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.1. Speciﬁc mechanisms of deformation and strength of nanostructured Ti-based materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2. Atomistic modeling of structure evolution, deformation and properties of ultraﬁne grained titanium . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3. Micromechanics of ultraﬁne grained and nanocrystalline titanium and alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3.1. Composite model of nanocrystalline materials and non-equilibrium grain boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3.2. Crystal plasticity model of UFG Ti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.3.3. Grain boundary sliding: analytical modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.4. Phase transitions in nanostructured nitinol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.4.1. Martensite lattice parameters and recovery strain in UFG Ti–Ni and Ti–Nb-based alloys: phase transformation theory analysis. . . 10
4.4.2. Thermomechanical modeling of martensitic transformation in nanostructured and UFG nitinol: effect of grain sizes and
their distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5. Biocompatibility and coatings for nanometal based implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.1. Biocompatibility of nanocrystalline Ti-based metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.1.1. Biocompatibility and corrosion behavior of Ti-based nanomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.1.2. Molecular dynamics modeling of dissolution and ion diffusion from the surface and GBs of Ti–Ni into body ﬂuid . . . . . . . 12
5.1.3. Experimental study of corrosion and ion release of nanostructured NiTi in physiological solution . . . . . . . . . . . . . . . . . . . . 13
5.2. Bioactive coatings and their effect on the mechanism of deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2.1. Role of bioactive coatings in Ti-based implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2.2. Deformation and strength of bioactive coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2.3. Multilevel modeling of strength and failure of nanostructured bioactive coatings on Ti-based biomaterials . . . . . . . . . . . . 14
5.3. Wear resistant TiN based PIRAC coatings on nanostructured Ti-based alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6. Potential for application: nanotitanium based implants with small radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7. Summary and conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1. Introduction
Due to rapid changes in the age structure of the world’s
population, an increasing number of people need their failed
tissues to be replaced by artiﬁcial implantable devices. Metallic
materials (primarily titanium and cobalt chrome alloys) are widely
used for surgical prostheses, such as joint replacements, mechani-
cal heart valves and dental implants. Although conventional
materials technology has resulted in clear improvements in
implant performance and longevity, rejection or implant failures
still happen. The increase in average life expectancy, as well as
rapid advances in modern surgery require new generations of
clinically relevant biomaterials, with enhanced biological and
mechanical performance. Advances in titanium manufacturing
technologies are expected to play an important role in the
development of the next generation of medical implants.
As forecast by a US Industry Study [1], titanium and titanium
alloys will provide the best growth opportunities among biocom-
patible metals in the years to come and will extend applications in
joint replacement systems, dental implants, fusion cages, stents,
mechanical heart valves, etc.
Nanostructuring by different processing techniques is one of
the promising directions in the development of Ti-based bioma-
terials with advanced properties. Computational modeling and
numerical testing can partially replace the expensive, time- and
labor-consuming mechanical and biological experiments and bring
nanostructured Ti-based materials closer to clinical realization.
2. Titanium as a material of choice for medical implants
For many decades, metallic biomaterials have been used
extensively for surgical implants due to the good formability and
high strength and resistance to fracture that this class of materials
can provide. The important disadvantage of metals, however, is their
tendency to corrode in physiological conditions, and a large number
of metals and alloys were found unsuitable for implantation as being
too reactive in the body. Therefore, the list of metals currently used
in implantable devices is limited to three main systems:
iron-chromium-nickel alloys (austenitic stainless steels), cobalt-
chromium-based alloys, and titanium and its alloys [2,3] .The advantages and drawbacks of metals used for implant
fabrication are presented in Table 1. From the point of view of
corrosion resistance, Ti is superior to other surgical metals, due to
the formation of a very stable passive layer of TiO 2on its surface. Ti
is intrinsically biocompatible and often exhibits direct bone
apposition. Another favorable property of Ti is the low elastic
modulus (twofold lower compared to stainless steel and Co–Cr),
which results in less stress shielding and associated bone
resorption around Ti orthopedic and dental implants. Furthermore,
titanium is more light-weight than other surgical metals and
produces fewer artifacts on computer tomography (CT) and
magnetic resonance imaging [4–7] .
The static and fatigue strengths of titanium, however, are too
low for commercially pure titanium (cp-Ti) implants to be used in
load-bearing situations. The addition of alloying elements, such as
aluminum and vanadium, allows for a signiﬁcant improvement of
the mechanical properties of titanium. Currently, Ti–6Al–4V is the
most widely used surgical Ti alloy. Despite the excellent passivity
and corrosion resistance of Ti–6Al–4V, elevated concentrations of
metal ions were detected in the tissues around the implants, as
well as in serum, urine, and remote tissue locations [8]. This slow
passive dissolution and accumulation of Al and V ions has long
aroused concerns regarding the long-term safety of Ti–6Al–4V
alloy implants. Aluminum is an element involved in severe
neurological, e.g. Alzheimer’s disease, and metabolic bone
diseases, e.g. osteomalacia, whereas vanadium ions were shown
to be potentially cytotoxic [9,10] . Moreover, accelerated release of
Al and V ions is expected to occur in tribocorrosion situations, due
to the simultaneous action of corrosion and wear [11]. Given their
inadequate wear resistance, Ti alloys are not used in conditions of
sliding contact, e.g. in articulating components of total joint
replacements. In many clinical situations, however, such as
femoral stem/ball contact of modular implants, stem/bone
interface of cementless implants or dental implant/bone interface,
enhanced release of Al and V ions from Ti–6Al–4V can take place
due to fretting (tribocorrosion involving micromotions). Therefore,
much effort is being directed toward the development of V- and
Al-free Ti alloys. The research on titanium alloys composed
solely of non-toxic elements has been under way for several years
[12].L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 2

An alternative approach to overcome the problem of harmful
ion release is to abandon the alloying concept altogether and to
enhance the mechanical properties of pure titanium by nanoscale
grain reﬁnement. The feasibility of strengthening different metals
by nanostructuring has been demonstrated in several studies
[13,14] . In addition to improved mechanical properties, a more
favorable cell response to nanostructured compared to coarse
grained titanium has been reported [15,16] .
A special group of Ti alloys that is gaining popularity in many
biomedical applications are Ni–Ti alloys (Nitinol) based on the
equiatomic intermetallic compound NiTi and containing 54–
60 wt.% Ni. Nitinol exhibits the unique properties of shape
memory and superelasticity that are utilized in stents, guide-
wires, embolic protection ﬁlters and other peripheral vascular
devices [17–19] . Due to the high titanium content, Nitinol alloys
exhibit good biocompatibility and corrosion resistance in vivo.
At the same time, the release of Ni ions is a concern as they may
cause allergic and carcinogenic effects as well alter cell behavior
[20,21] .
In addition to shape memory, Nitinol, in its martensitic state,
exhibits a very low elastic modulus – less than half that of pure
titanium. This makes Nitinol an attractive candidate material for
orthopedic, spinal and dental implants since low stiffness
minimizes the stress shielding of the peri-implant bone. These
new applications will require enhanced mechanical and physical
properties (higher strength, tighter transformational hysteresis,
etc.). It has been reported in several papers that nanostructuring of
Nitinol can lead to a signiﬁcant improvement in its shape memory
and strength characteristics [22–25] .
To summarize, the use of titanium-based implantable devices
has become an integral part of modern medicine. Nanostructuring
is a promising way to further improve the safety, effectiveness and
longevity of medical implants made of these materials.
3. Nanostructuring of titanium and Ti alloys: concept and
technologies
3.1. Nanostructuring of titanium and Ti alloys
Nanostructuring of titanium and Ti alloys opens new possibili-
ties for improving the long-term performance of medical implants
[26–28] .
Still, requirements toward nanostructuring technologies to be
used for the production of medical implants are rather high. The
technologies should allow the efﬁcient and affordable fabrication
of bulk samples with homogeneous microstructures, without anydefects. The nanostructured specimens should retain their
microstructures even after the samples are coated or installed.
One of the most efﬁcient methods of fabrication of bulk
nanocrystalline materials is the metalworking technology called
‘‘severe plastic deformation’’ (SPD) [13]. The SPD concept is based
on the fact a metal specimen subjected to high plastic strains with
complex stress state, very high hydrostatic pressure and very high
strains leading to breaking the coarse grains down into ultra-ﬁne
(with a size of 100–1000 nm) or nano-sized (with the size less than
100 nm) grains. Thus, the SPD has been referred to as ‘top-down’
approach. The main techniques of SPD processing of metals
include:
(1) Equal channel angular extrusion (ECAP). The ECAP technique
imposes large plastic deformation on a large billet by simple
shear [29]. The billet is pressed through a special die which has
two channels having the same cross sections and intersecting
at an angle in the range of 90–120 8. The billet can be subjected
to several ECAP passes in order to increase the total strain
introduced into the billet. It should be noted that the ECAP-
Conform technique was developed in the last decade for
producing very long rods [29–31] .
(2) High pressure torsion (HPT). In HPT, a small disk is placed
between two anvils and one of them is able to rotate under
pressure of several GPa, thus, deforming the disk by pure shear
[32]. Even hard to deform metallic materials can be subjected
to HPT processing due to very high pressures applied. Two
shortcomings of this SPD technique include small size of the
specimens which can be processed and microstructure
inhomogeneity along the disk radius [32].
(3) Accumulative roll bonding (ARB). It is a method of rolling a
stack of metal sheets, which is repeatedly rolled to a severe
reduction ratio, sectioned into two halves, piled again and
rolled [33]. It should be noted that ARB involves not only
deformation, but also bonding (roll bonding). Only sheets can
be produced via ARB method.
(4) Hydrostatic extrusion (HE) is another technique which has
been utilized for grain reﬁnement in metallic materials. In the
HE process, the billet is surrounded by a pressurized liquid,
except the area of contact with die [34]. This process can be
done hot, warm, or cold, however the temperature is limited by
the stability of the ﬂuid used. The process must be carried out in
a sealed cylinder to contain the hydrostatic medium. The main
advantages of the HE processing are absence of any friction
between the container and the billet and even ﬂow of material.
This allows faster processing speeds, higher reduction ratios,
and lower billet temperatures.Table 1
Overview of metals used for implantable medical devices.
Metal/alloy Advantages Drawbacks
Stainless steel 316 L High ductility, good machinability, high wear resistance. Fatigue strength lower than of other implant alloys. High
elastic modulus (possibility of stress shielding). Inferior
corrosion resistance and biocompatibility compared to
other implant alloys. Relatively high metal ion release and
adverse host response.
Cobalt–chromium (CoCr) based alloys High static and fatigue strength. High wear resistance. High
corrosion resistance and good biocompatibility.High elastic modulus (possibility of stress shielding). Less
corrosion resistant and biocompatible than Ti alloys.
Adverse host response to released metal ions (Ni, Cr).
Commercially pure (cp) titanium Excellent corrosion resistance, better than of any other implant
metal (due to TiO 2surface oxide). High biocompatibility, direct
bone apposition. Relatively low elastic modulusStatic and fatigue strength too low to be used in load-
bearing implants. Poor wear resistance.
Ti–6Al–4V alloy Excellent corrosion resistance. High biocompatibility, direct
bone apposition. High static and fatigue strength. Relatively
low elastic modulusPoor wear resistance. The release of Al and V ions may cause
health problems.
NiTi (Nitinol) Shape memory and superelastic effects. Low stiffness. Good
corrosion resistance and biocompatibility.Adverse host response to released Ni ions. Poor wear
resistance. Complex fabrication process.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 3

Many other SPD processing techniques have been developed
[29] and a detailed list of these methods can be found in a recent
comprehensive overview [35]. Application of all these technologies
lead to the formation of high density of crystal lattice defects in the
microstructure, their rearrangement into cells and subgrains,
followed by increase of misorientation of low angle grain
boundaries into high angle grain boundaries and, thus, formation
of ultra-ﬁne- or nano-grained microstructure [13,36,37] . Various
SPD methods have been successfully applied for grain reﬁnement
in pure Ti and Ti-based alloys [27,37,38–47] .
In Table 2, the mechanical properties of bulk nanostructured
titanium and several Ti-based alloys produced via various SPD
techniques are given. These data clearly demonstrate that the
strength characteristics of pure nanostructured titanium are
signiﬁcantly higher than those of cp-Ti of the same grade and
are comparable with (and in many cases, higher) those of
commercial Ti–6Al–4V alloy. Importantly, the ductility of nano-
structured titanium and Ti–6Al–4V is only slightly compromised
by the SPD processing.
Severe plastic deformation is also an effective tool for
fabricating ultra-ﬁne grained (UFG) and nanostructured Ti–Ni
(nitinol) SMAs which exhibit enhanced mechanical properties. In
addition, grain reﬁnement down to ultra-ﬁne scale has been shown
to affect the phase transformation temperatures of Nitinol [51–54] .
NiTi alloys subjected to HPT and ECAP demonstrate high recovery
stresses and shape recovery of up to 10% [55], along with higher
plateau stress and reduced fracture strain.
Alternatively to SPD processing, bulk nanocrystalline titanium
and Ti alloys can be fabricated from nanosize powders, by high
pressure consolidation at temperatures close to ambient. In this
process, also called Cold Sintering, the high applied pressure
results in severe plastic shear deformations of powder particles
that are consolidated into a fully dense bulk material [56–58] . The
fabrication of dense nanostructured Fe, Ni, Al and Cu metals, as
well as Ni–TiC and Cu–TiN nanocomposites by cold sintering of the
corresponding nanosize powders was reported [59,60] . In Ref. [61],
micron-submicron Ni, Co and Fe intermetallics were fabricated by
solid state synthesis of cold sintered elemental nanopowder
blends. Full density and high mechanical properties were reported
for cold sintered nanostructured rapidly solidiﬁed powders of Al
alloys and high speed steels [62].
As seen from the above, nanostructuring of Ti-based materials
for medical implants can provide them with improved mechanical
properties and biocompatibility. SPD-based technologies have
proven effective in the processing of nanostructured titanium,
nitinol and other Ti-based alloys and already ﬁnd their way into the
dental implant industry [27]. Still, further developments in the
current nanostructuring technologies of Ti-based alloys arerequired to make these materials suitable for other demanding
medical applications, such orthopedic, spine and cardiovascular
surgeries.
In this and following sections, we describe some works directed
toward the optimization of SPD technologies for the fabrication of
nanostructured Ti and Ti-based implants. Furthermore, we review
methods of computational modeling of nanoscale mechanisms of
plastic deformation, strength and biocompatibility of nanostruc-
tured Ti and Ti alloys.
3.2. Severe plastic deformation: processing routes and microstructure
evolution. Multiscale computational modeling
The formation of nanocrystalline structures in titanium speci-
mens is a result of high hydrostatic pressure and shear stresses of
titanium rods under SPD treatment. The quality of the nanos-
tructures, grain size distribution, average grain sizes, grain
boundary properties and other microstructural parameters
strongly depends on the parameters of thermo-mechanical
processing (temperature, strain rate, pressure, etc.).
In order to study the interrelationships between the SPD
processing parameters and formed microstructures, multiscale
computational models of the SPD process are employed. A number
of models considering the engineering aspects of SPD, and, on the
other side, the dislocation and nanoscale mechanisms of
microstructure evolution under SPD have been developed (see
overviews e.g. [63–65] ). In order to study the macro-micro-nano
and technology-physics interrelations in the SPD process, a
multiscale model of SPD process was developed [66]. First, the
plastic ﬂow of the material during SPD (ECAP) was modeled using
Deform 3D software, with real technological parameters. This
allowed one to evaluate the stress and strain ﬁelds. It was
concluded that the strain intensities in a billet in the longitudinal
and cross section was rather uniform at the chosen parameters of
ECAP.
Further, a multiscale FE model has been developed, which
allowed one to analyze the evolution of microstructure (grain size,
dislocation density, vacancy concentration) and texture as well as
mechanical properties in pure Ti after ECAP-C processing leading to
formation of nanostructure.
On the macro-level, a FEM-model for ECAP-C processing of Ti
was developed which takes into account various processing
parameters (die-set design, temperature, friction coefﬁcient,
processing speed, processing route, etc.). On the meso-level, a
CP model (visco-plastic self-consistent model) was used to
calculate texture evolution in pure TI during ECAP-C processing
as well as to simulate deformation behavior of polycrystalline
Ti under given loading condition. This procedure providesTable 2
Mechanical properties of nanostructured titanium and Ti-based alloys produced via various SPD techniques compared to cp-Ti and conventional Ti–6Al–4V alloy.
Material Processing method Grain size s0.2[MPa] sUTS[MPa] eu[%] ef[%] Reference
cp-Ti (grade 2) Conventional Several microns 275 345 20 [49]
cp-Ti (grade 4) Conventional Several microns 485 550 15 [49]
Ti ECAP 280 nm 640 710 – 14 [38]
Ti (grade 2) ECAP + cold rolling 150–200 nm 970 1080 2.4 32 [38]
Ti (grade 2) ECAP + forging + drawing 50–300 nm /C241000 /C241080 – – [41]
Ti (Grade 4) ECAP-C + swaging 150 nm 1190 1250 1.6 11 [42]
Ti HPT 120 nm 790 950 14 [43]
Ti (Grade 4) ECAP + swaging + drawing 200 nm 1220 1280 3.7 10.1 [48]
Ti–6Al–4V Mill annealed Several microns 795–875 860–965 10–15 [49]
Ti–6Al–4V ECAP + extrusion + annealing 250 nm 1310 1370 4.0 12.0 [44]
Ti–6Al–4V Multiple forging 200–300 nm 1180 1300 0.5 7 [45]
Ti74Nb26 ECAP 200–300 nm – 750 1–2 7–8 [46]
Ti49.4Ni50.6 HPT + annealing 20–30 nm 1570 2620 – 6 [47]
Ti49.8Ni50.2 ECAP – 1360 1410 – 23 [50]
Ti49.8Ni50.2 ECAP + cold rolling – 1900 2000 – 10 [50]L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 4

information on slip system activity and output textures affecting
mechanical properties of the material.
On the micro-level, a disclination criterion for grain subdivision
has been developed taking into consideration the grain reﬁnement
process which leads to formation of nanostructure in the processed
Ti. These three approaches have been coupled into one uniﬁed
simulation scheme where deformation history from the macro-
level and the data on grain subdivision from the micro-level have
been used in VPSC modeling procedure on meso-level. The
nanostructured Ti was described using the kinetic dislocation
approach, which allowed to obtain information on the microstruc-
ture parameters (grain size, dislocation density) and mechanical
properties (strength and ductility).
Fig. 1 illustrates distribution of shear strain in a Ti billet after 4
ECAP-C passes obtained from the FEM-model. It is seen that shear
deformation is quite homogeneously distributed along the
processed billet.
Further, the modeling of deformation behavior and microstruc-
ture evolution was performed for nano-Ti produced via ECAP-C for
6 passes with and without extra drawing. It was found that the
nano-Ti after ECAP-C processing and drawing shows higher yield
strength due to higher total dislocation density. However, this
material has a lower ductility due to the lower density of mobile
dislocations in the grain interior.
In the nano-Ti obtained via ECAP-C processing and drawing, the
increase of vacancy concentration during sample deformation is
lower compared to that in the nano-Ti obtained via ECAP-C
processing. The vacancies play a more important role in annihila-
tion of dislocations during plastic deformation of the ECAP-C
processed and drawn nano-Ti. The non-equilibrium character of
grain boundaries increases during plastic deformation due to
increasing density of grain boundary dislocations; the density of
forest dislocations increases, too.
The main mechanism of the nanoscale structure formation
during severe plastic deformation is the grain subdivision. In Ref.
[67], a computational model of grain subdivision based on the
balance equations for the evolution of dislocation and disclination
densities with accumulated plastic strain was developed. These
equations include physically based terms for the generation,
storage and annihilation rates of the respective lattice defects. It
was assumed that orientation fragmentation during the deforma-
tion is triggered by intragranular strain localizations. Prismatic,
basal and pyramidal slip as well as screw and edge dislocations
are treated separately; partial disclination dipoles arise from
intersections of slip bands with grain boundaries. Scaling laws are
used to calculate cell and fragment sizes from the immobiledislocation and disclination densities. The model allows reprodu-
cing substructural parameters in the order of magnitude that is
found experimentally after large strains, and predicts the onset of
massive orientation fragmentation.
3.3. Novel thermomechanical ECAP processing route for fabrication of
nano-Ti with very homogeneous structure and superior properties
The analysis of the data presented in Table 2 shows that
application of complex SPD processing routes consisting of 2–3
operations (for example, ECAP combined with cold rolling, ECAP
combined with swaging and drawing, etc.) leads to smaller grain
size and, thus, to higher mechanical strength. In order to improve
the technology of nanotitanium rod fabrication to satisfy the
requirements for the dental implants, a novel complex SPD
processing route for fabrication of high strength nano-Ti was very
recently developed on the basis of the computational analysis of
the fabrication regimes and structure evolution relationships [42].
The newly developed technology foresees that Ti billets with cross
section of 11 mm /C2 11 mm are subjected to ECAP-C processing at
200 8C for 6 passes followed by drawing at 200 8C into cylindrical
rod having a diameter of 6 mm. Thus, obtained rods show the yield
strength of 1190 MPa and ultimate tensile strength of 1250 MPa at
room temperature and these properties are retained at tempera-
ture of human body. Such signiﬁcant increase of mechanical
strength was related to formation of a very homogeneous ultra-
ﬁne grained microstructure with equiaxed grains having the
average grain size of /C24150 nm and to development of a
crystallographic ﬁber texture with the c-axis perpendicular to
the rod axis and (10–10) direction parallel to the rod axis (Fig. 2).
The latter was conﬁrmed via crystal plasticity modeling of drawing
process in this processing route [68]. This new processing route for
producing nano-Ti was also simulated using the polycrystalline
simulation. The model initial conditions were the texture of the
billets after 6-ECAP passes assuming a high angle GB misorienta-
tion between grains. The drawing process was then simulated and
the results showed that the polycrystalline CP models were able to
accurately predict the ﬁnal texture, mechanical anisotropy and
grain shape evolutions in rods [68].
From the viewpoint of commercialization, this new SPD
processing route is characterized by relatively low cost due to
the fact that ECAP-C is a continuous processing technique
developed for fabrication of long-length (up to 3 m) rods, so the
wastage of material in this processing operation is dramatically
reduced [29,30] . It should be also noted that no additional
metalforming operations are required for fabrication of dental
implants from the processed rods: The near net-shape parts can be
readily cut off from the processed rods and machined into dental
implants with low wastage of material. So, the newly developed
technological route represents a promising approach for the
development of stronger Ti-based materials for medical implants.
3.4. Thermomechanical treatment of UFG Ti–Ni alloys
As shown in Refs. [23–25,69] , the nanosubgrained and
nanocrystalline shape-memory alloys (SMA) structures can be
efﬁciently fabricated with the use of the technology called TMT
(thermomechanical treatment [70–75] ). This technology com-
prises of cold working (CW) and post-deformation annealing
(PDA). The TMT represents in fact a version of ECAP, where the
loading conditions are deﬁned by large applied strains at rolling
(instead of pressure and numbers on runs, deﬁned in ECAP). To
analyze the structure of TMT-processed Ti–Ni SMA, TEM studies
of the materials after TMT were carried out. It was observed that
a cold rolling (CR) with moderate deformation (true strain
e = 0.3–0.5) of Ti–Ni SMA creates a well-developed dislocation
Fig. 1. Distribution of shear strain in Ti billet after 4 ECAP-C passes.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 5

substructure of B2-austenite, which is gradually replaced by a
mixed nanocrystalline plus amorphous structure during further
deformation [72,73] . The PDA in a certain temperature range
leads to nanostructures formation (Fig. 3; here is Ti-50.26 at.% Ni
SMA annealed at 400 8C for 1 h after CR with various strains in
the range from e = 0.3 to 1.9). A nanosubgrained polygonized
substructure with subgrain size below 100 nm forms as a result
of polygonization in the dislocation substructure of moderately
deformed alloy, while a nanocrystalline structure with grain size
below 100 nm forms as a result of the amorphous phasecrystallization and initial nanograin growth in the severely
deformed alloy [72]. PDA after CR with intermediate strains
creates a mixed nanosubgrained + nanocrystalline structure
(ﬁfty-ﬁfty when CR strain is about e = 0.75–1.0). Such TMT
regimes drastically increase strength parameters and both
maximum recovery stress and completely recoverable strain,
the latter are the main functional properties of SMA (Fig. 4).
Thus, TMT allows to obtain the nanocrystalline Ti-based shape
memory allots, with enhanced strength and mechanical
properties.
Fig. 2. Microstructure and texture of commercially pure Ti after ECAP-C processing in 6 passes and drawing: (a) bright ﬁeld image; (b) dark ﬁeld image of the same place; (c)
experimental pole ﬁgures (10–10), (0 0 0 2), (10–11) and (11–20).
Fig. 3. Typical structure for Ti–Ni alloy after cold rolling (e = 0.3–1.9) and post-deformation annealing at 400 8E (in Ti–50.26%Ni).L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 6

3.5. Comparison of cold sintering and ECAP processing routes of
nanostructuring Ti-based materials
As it was mentioned in Section 3.1, cold sintering or high
pressure consolidation of powders at temperatures close to
ambient resulting in severe plastic shear deformations and in
many cases in full density [56–58] may be an alternative method
for processing of nanostructured metals and composites in general
and Ti based materials in particular.
In the present research, cold sintering was employed for the
processing of submicron-nanoscale pure Ti and NiTi SMA. To produce
pure Ti, submicron titanium hydride (TiH 2) powder was ﬁrst
compacted to 70% density and dehydrogenated in vacuum at
600 8C for 1 h. Subsequent cold sintering at 300 8C at the pressure of
3 GPa yielded near-fully-dense titanium with grain size in the range
150–250 nm. The microhardness of the obtained specimens was
3600 MPa and their yield strength in compression – 720 MPa. The
latter value is close to the yield stress of titanium processed by ECAP
[38]. For the processing of NiTi, submicron Ni powder was ﬁrst
treated in hydrogen ﬂow at 300 8C to remove the surface oxide and
then blended with submicron TiH 2powder (at 1:1 atomic ratio of Ti
and Ni). The blend was then subjected to high energy attrition milling
to further reﬁne the submicron TiH 2and Ni particles and to achieve
their homogeneous distribution. 70% dense TiH 2–Ni compacts were
dehydrogenated at 600 8C for 1 h, cold sintered at 3 GPa, 300 8C and
vacuum annealed at 700 8C. According to XRD analysis, 4 h at 700 8C
were enough to transform the dense blend of Ni and Ti into the NiTi
intermetallic (nitinol). The specimens obtained were near fully dense
with grain size in the range of 100–150 nm.
The results of our experiments show that cold sintering of ultra-
ﬁne powders is a feasible route for the fabrication of nanostruc-
tured Ti based alloys including nitinol. The potential advantage of
cold sintering over ECAP is the possibility of fabricating Ti-based
nanocomposites with improved mechanical and biological perfor-
mance introduction of bioinert and bioactive nanoparticles. The
mechanical properties of cold sintered specimens can be further
enhanced by subjecting them to severe plastic deformation. More
research is needed to optimize the cold sintering processing
parameters of nanostructured Ti and Ti based alloys.
4. Superior mechanical properties of UFG titanium-based
materials: computational modeling
Mechanical and biological properties of nanostructured mate-
rials are controlled by a number of physical processes, which actand interact at many scale levels, from atomistic to the
macroscopic level, and via various interacting physical mecha-
nisms. The development of new metallic nanomaterials for
medical applications and determination of the optimal composi-
tions, fabrication technologies and micro/nanostructures require
complex, very expensive and labor consuming experiments along
with in vitro (cell culture) and in vivo (animal model) studies.
In order to improve the materials properties, and to determine
the optimal microstructures, production regimes and technologies,
as well as to reduce animal experimentation, reliable computa-
tional models for the virtual, numerical testing of these materials
are necessary.
The models, linking the scale levels, physical and mechanical
processes with the output service properties of the materials,
should provide computational tools for the analysis of the
already available and the design of new, improved nanomater-
ials for medical applications, The models should allow both the
predictions of their usability, mechanical properties, biocom-
patibility, and the optimization, microstructure design and
development of new materials on the basis of virtual testing on
the materials.
In this section, main approaches and concepts for the
computational modeling and virtual testing of nanocrystalline
and ultraﬁne grained materials are considered.
4.1. Speciﬁc mechanisms of deformation and strength of
nanostructured Ti-based materials
Nanostructured materials are characterized by a number of
speciﬁc features which distinguish them from regular, coarse
grained metals.
Among them, one can mention the following effects: superior
yield strength (up to 5–10 times higher than of coarse-grained
materials), deviation from Hall–Petch relation at ultraﬁne and
nanoscale grain sizes (below 100 nm), which goes into negative
Hall Petch slope at about 10 nm [76,77] , high volume of highly
disordered grain boundaries, enhanced strain rate sensitivity of
mechanical properties, dependent on grain size; asymmetry of
tensile and compressive behavior at small grain sizes [78]; super-
ductility at room temperatures, deformation mechanisms different
from those the case of coarse grained materials.
Among the observed plastic deformation mechanisms, one can
mention, apart from the usual dislocation glide, grain boundary
sliding, diffusion controlled creep (Coble model) and Nabarro–
Herring creep (through lattice diffusion) [78–81] . These mechanisms
Fig. 4. Functional properties of Ti-50.0%Ni alloy with recrystallized (RS), nanosubrained (NSS) and nanocrystalline (NCS) structures.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 7

and effect can be observed for different grain sizes and strain rate
ranges.
The knowledge of interrelations between nanoscale deformation
and strength mechanisms and the service properties of the materials
is the way to ﬁnd the reserves of optimization, improve the
fabrication technology or predict the service properties of nano-
materials. When analyzing the mechanical properties of nanostruc-
tured metals, one should take into account the peculiar mechanisms
of deformation, the role of the grain boundary phase, the
mechanisms of grain boundary sliding and diffusional mass transfer.
4.2. Atomistic modeling of structure evolution, deformation and
properties of ultraﬁne grained titanium
The straightforward way to simulate the physical and
mechanical properties of nanostructured materials is to use
atomistic approaches and derive the mechanical and service
properties from the atomistic, molecular statics and molecular
dynamics simulations.
Most accurate molecular dynamics techniques are based on
numerical solution of the Schro ¨dinger equation for the description
of interactions within the system (see, e.g., [82,83] and references
therein). However, such ab initio approaches are extremely
demanding computationally and currently can be performed only
for the systems of few hundreds of atoms at the picosecond
timescale. An alternative to the ab initio methods are the classical
MD simulations which describe the time-evolution of a system by
integrating classical equations of motions using the deﬁned
interactions between the constituent atoms. Using this technique
one can ultimately describe the dynamics of up to 107atoms at the
nano- and microsecond timescales. Within the framework of this
scheme the interactions of atoms are parameterized by use of
various empirical potentials or the force ﬁelds. To a great extent,
the success of the MD simulations depends on the availability and
reliability of the interatomic potentials. Recently, the MD studies
have been carried out to analyze the phase transformations in Ni–
Ti alloys [84,85] . In the series of papers [84,86] the structural
change in Ni–Ti alloys under martensite and amorphous trans-
formations was analyzed using the interatomic potentials obtained
within the frameworks of the embedded atom method (EAM) [87]
and of the modiﬁed EAM [88]. The EAM potential was built by
ﬁtting a number of experimental constants and the values obtained
in ab initio calculations [89]. The approach used in Ref. [84] was
based on atom-by-atom detection of speciﬁc phases by means of
common neighbor analysis [90]. In Ref. [97], Yamakov and
coworkers carried out the MD simulation of nanocrystalline nickel
with the random orientations of the crystals, and the defect-free
interiors of the grains. The simulations with 105–106atoms were
performed. Van Swygenhoven et al. [96] studied the inﬂuence of
grain boundary structure on plastic deformation of nanostructured
Ni and Cu. The MD simulations indicated the presence of a critical
grain size below which all plastic deformation was accommodated
in the grain boundaries and no intra-grain deformation was
observed. Kadau et al. [91] performed a molecular dynamics study
of nanocrystalline Al undergoing tensile loading. In Ref. [85,92]
(see also [93]) the crystal structure of martensitic NiTi was studied
by means of ﬁrst-principle calculations based several density
functional theory (DFT) implementations. The MD was further
performed based on the derived interatomic potentials. It was
noted that the success of the consequent MD calculations of NiTi
alloys strongly depends on the accurate choice of the interatomic
Ti–Ti, Ni–Ni, and Ni–Ti potentials. In Ref. [66], a quantum-
mechanical evaluation of elastic properties of Ti was carried out on
the basis of ﬁrst principle approach. A set of quantum-mechanical
calculations of different crystalline Ti structures were performed
using density functional theory (DFT) within a plane-wavepseudopotential approach, implemented in ABINIT package. The
exchange and correlations energy functionals were described
either within the local density approximation (LDA) or the
generalized gradient approximation (GGA). The bulk modulus
obtained within GGA + U approach is in agreement with other
theoretical calculations and with the experimental data.
In Ref. [94], the deformation mechanisms under tensile loading
and indentation, loading rate effect and plasticity initiation were
analyzed using the molecular dynamics. In order to include the effect
of grain boundaries and interfaces, the authors [94] used a model
with a symmetrical tilt grain boundary under tensile loading. The
cell size was /C24100 A˚/40,000 atoms in length. In the simulations it
was observed that the potential energy of Ti increases monotonically
with deformation up to some threshold strain level. After the
initiation and development of plastic deformation, the energy
decreases in an avalanche-like manner. With growing loading rate,
the rate of potential energy decrease becomes lower, which is
attributed to the local structural transformations being incapable of
accommodating the growing stress levels in the crystallite. The
change in the curve shape observed for the threshold strain level is
attributed to the generation of structural defects (dislocations)
induced by thermal ﬂuctuations.
Also, the particle method (molecular dynamics approach based
on the movable cellular automaton techniques) was applied to
study the deformation mechanisms in nanotitanium under
nanoindentation [95]. The indentation curve in this case is
characterized by a periodic occurrence of kinks, which correlates
with the interplanar spacing of the crystallite in the direction of
indenter penetration. As soon as the penetration depth of about
4.5 A˚is reached, partial dislocations start forming, ﬁrst under the
indenter tip and later on in the glide plane (0 0 0 1) in the direction
of crystal side, thereby creating stacking faults and causing steps
formation on the free surface.
4.3. Micromechanics of ultraﬁne grained and nanocrystalline
titanium and alloys
4.3.1. Composite model of nanocrystalline materials and non-
equilibrium grain boundaries
While the atomistic, molecular dynamics methods allow one to
analyze the basic, physical properties of the nanomaterials
behavior, they can be used still only for modeling relatively small
volumes and over small time ranges. That is why there is a
necessity to use mechanics methods to simulate the meso- and
macroscale nanomaterials behavior and service properties.
In so doing, the main assumption is that the atomistic scale,
nanoscale processes can be approximated and modeled by
mechanical elements [98,100,101] . This assumption is not apparent,
and should be validated by experiments and atomistic simulations.
Quite often, the application of micromechanics in the analysis of
nanomaterials is based on the composite model. A material is
considered as consisting of two phases: grains with bulk properties
and the boundary phase, represented as an amorphous glass
material [98,99] . In the series of works based on the composite
model, the rule-of-the mixture approach [99], FEM models and unit
cells [102,103] , other composite models were used. Li et al. [98]
developed a phase mixture based ﬁnite element model of
nanocrystalline nickel, based on the digital topological model of
the real microstructure, which followed the experimental observed
log-normal distribution and including the rate-dependent amor-
phous constitutive model for the grain boundary sliding behavior.
An important feature of UFG materials, which has effect on their
mechanical and strength properties, is the availability of non-
equilibrium grain boundaries. Non-equilibrium grain boundaries
(NEGBs) are GBs with higher energies, large area density of GB
dislocations, higher diffusion coefﬁcient, larger free volume andL. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 8

other effects. There are a number of different formulations and
explanations of the physics of NEGBs [37,104–107] . Tucker and
McDowell [105] characterized the degree of non-equilibrium by
excess interfacial free volume (IFV). They demonstrated that the
tensile strength is lowered as a function of increasing NE state of GBs.
Resistance to GB sliding and migration decreases with increasing IFV,
under shear (/C2430–50% higher peak shear strain for EGB than for NEGB,
and 25–30% higher tensile stress). Amouyal and Rabkin determined
the relative GB energies in UFG Cu employing the thermal grooving
technique and demonstrated that certain degree of non-equilibrium
is retained by the GBs even after recrystallization [110] .
Part of the NE effect is related to the concentration of alloying
elements and formation of precipitates near boundaries, which
might increase the critical stresses necessary for nucleation of new
dislocations at the boundaries and/or for their motion.
In order to analyze the effect of NEGB on the material
deformation, Liu et al. [108,109] studied the inﬂuence of changed
diffusion coefﬁcient in GBs, high initial dislocation density in GB and
the availability of regions of changed properties due to segregation
and/or precipitate of alloying elements on the mechanical properties
of UFG Ti. The studies were carried out numerically using the
composite model of nanomaterials (with grain boundaries as layers
of second phase) and the ABAQUS subroutine VUMAT based on the
dislocation density evolution model of GB deformation.
The dislocation density based model included the effects of
dislocation accumulation and annihilation, local storage (ﬂux of
mobile dislocations) and immobilization at stored dislocations,
mutual annihilation of dislocations of opposite sign, and, for GBs, a
second annihilation mechanism, where two stored dislocations of
opposite sign may climb toward each other and annihilate. As a
result of the series of numerical simulations, it was demonstrated
that the non-equilibrium of GBs leads to the increase in the yield
stress. Yield stress increases with decreasing the diffusion
coefﬁcient slightly: when the diffusion coefﬁcient increases by
factors 100 and 1000 (at the grain size 50 nm), the yield stress
increases by 47 and 98%, respectively. An increase in the initial
dislocation density (DD) in the GBs by a factor of 1000 (i.e., from
1015to 1018m/C02) leads to about 2 times higher yield stress, while
the increase by a factor of 100 (i.e., from 1015to 1017m/C02) leads to
40% higher yield stress (for nTi with average grain size of 50 nm).
The differences are much smaller for the titanium with average
grain size of 250 nm: they are roughly 20% and 4%, respectively.
Precipitates/foreign atoms (e.g., oxygen and carbon precipitates) in
the GB lead to the increased yield stress, by 16% (precipitations
randomly arranged in GB) or 28% (precipitations on GB/GI border).
Thus, the micromechanical models of nanomaterials allow to
analyze some important effects of the nanomaterials deformation
and to explore reserves of the optimization of the materials.4.3.2. Crystal plasticity model of UFG Ti
An important factor inﬂuencing the mechanical properties of
nanotitanium is the misorientation of grains and the availability of
high angle GBs. The modeling of the mechanical behavior of
nanomaterials at the level of grains, dislocations and dislocation
arrays is carried out with the use of the methods of crystal plasticity
[111–117] . The introduction of the size effects in the crystal
plasticity models has been accomplished through the use of strain
gradient single crystal plasticity (SGSCP) models. Nye [118] and
Ashby [119] explained the ‘‘Smaller is Stronger’’ phenomenon as
the result of the interaction between statistically stored dislocations
(SSDs, responsible of plastic strain) and geometrically necessary
dislocations (GNDs, responsible of plastic strain gradients). The size
effect was simulated with the use of phenomenological strain
gradient models that incorporate the inﬂuence of a characteristic
length of the material in the constitutive equations of isotropic
materials [120–123] . This characteristic length was related to some
microstructural characteristic as the distance between precipitates,
voids, etc. The extension of these phenomenological models to
crystal plasticity [124,125] resulted in the so-called ‘‘strain gradient
crystal plasticity models’’ that account for both plastic anisotropy
and size effects. The size dependency of the plastic ﬂow has a great
inﬂuence in the mechanical response of polycrystals, and the special
characteristics of nano-grained materials cannot be always
explained by the dependency of the ﬂow stress with the grain size
(Hall–Petch effect).
In Ref. [68], the crystal plasticity approach was used to
construct a bottom-up model linking nanoscale to the continuum
scale, what will allow taking into account the real microstructures
of the material. A crystal plasticity (CP) model of nTi was developed
taking into account the grain orientation distribution.
The effective properties of polycrystalline nano-Ti were deter-
mined by means of the FE simulation of an Representative Volume
Element (RVE) of the microstructure. Two different representation of
the microstructure were used: a voxel-based model in which the
RVE is made up by a regular mesh of N /C2 N /C2 N cubic ﬁnite elements
and each of them stands for a Ti grain, and a model where each
crystal is represented with many elements (Fig. 5). In either RVE of
the polycrystal, the orientation of each grain was determined from
the input orientation distribution function (ODF) which describes
the initial texture using a Monte Carlo method. The models were
validated experimentally.
In order to predict the evolution of texture, the drawing process
was simulated. The simulations of nano-Ti billets after 6 ECAP-C
passes subject to drawing to produce rods with the longitudinal
axis oriented in the billet longitudinal direction were carried out.
The analysis showed that the models allow to predict pole ﬁgures
and microstructure evolution in rods.
Fig. 5. Representative volume elements of polycrystalline Ti. (a) Voxel model with 1000 cubic FE in which each one stands for a single crystal. (b) Realistic RVE containing 100
crystals discretized with 64,000 cubic ﬁnite elements. (c) Comparison of curves.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 9

In these investigations, computational models of deformation
of UFG titanium at nanoscale were developed, and a number of
special effects in plastic deformation in nTi were studied: the effect
of orientation distribution, textures, non-equilibrium grain
boundaries, diffusion coefﬁcients and precipitates on the defor-
mation behavior, grain subdivision and interaction between grain
boundary sliding, diffusion and dislocation nucleation. These
models and studies should serve as a basis for further improve-
ment of UFG materials and technologies of their processing.
4.3.3. Grain boundary sliding: analytical modeling
Grain boundary sliding becomes increasingly important in bulk
ultraﬁne grain (grain size in the range 100–1000 nm) and
nanocrystalline (grain size below 100 nm) materials, and nano-
structured coatings and thin ﬁlms [126–132] . For example, in the
study of Ke et al. [130] relative grain rotations of up to 158 were
observed in thin Au ﬁlms with the average grain size of 10 nm in
situ tested in tension in the high resolution transmission electron
microscope (TEM) [130] . The absence of any dislocation activity in
the ﬁlm led the authors to the conclusion that GB sliding represents
the main room temperature plasticity mechanism in this range of
grain sizes. A reversible, non-linear elasticity of thin free-standing
Al and Au ﬁlms was also attributed to grain rotations and GB
sliding [131] . These and numerous other observations of GB sliding
are backed up by atomistic computer simulations which indicate
the increasing role of GB sliding and grain rotations with
decreasing grain size in nanocrystalline materials [133–135] . GB
sliding, together with Coble creep controlled by GB diffusion are
often named as the underlying mechanisms responsible for the
inverse Hall– Petch effect (the decrease of hardness and yield stress
of nanocrystalline material below a critical grain size [136] ). An
important aspect of plasticity controlled by GB sliding is a
necessity to accommodate changing grain shapes. Moreover, the
GBs themselves are rarely planar and exhibit numerous facets and
undulations, which also can hinder the sliding process. The GB
sliding-related shape accommodation can be diffusional, elastic, or
plastic. Diffusional accommodation is controlled by the GB
diffusion and is closely related to Coble creep. Raj and Ashby
developed a model of GB sliding controlled by diffusion
accommodation and obtained a relationship for the sliding rate,
du/dt [136] , which is often employed in estimates of GB sliding
contribution to the plasticity of nanocrystalline materials. While
plastic accommodation is dominated by the activity of dislocation
sources and conventional dislocation glide in coarse grain
materials, nucleation and/or glide of partial dislocations (some-
times accompanied by twinning) is a dominating plasticity
mechanism in nanocrystalline materials [133–135] . The partials
nucleate at the GB, glide very fast through the small grain, and
annihilate at the opposite GB. Finally, the elastic accommodation of
GB sliding is very important in nanocrystalline materials because
of their high yield stress and high level of internal elastic stresses
that can be achieved during deformation.
GB sliding can be phenomenologically described as a viscous
Newtonian ﬂow. This process, as well as GB dislocation movement
involving climb, are thermally activated; that is why GB sliding in
coarse grain polycrystals plays a signiﬁcant role in deformation
only at elevated temperatures above approximately 0.4Tm, where
Tmis the melting point of the material.
Since the diffusion coefﬁcients along the triple junction are
much higher than along the GBs [137] , the triple junctions can
provide an additional diffusion route contributing to the accom-
modation of GB sliding. In Ref. [66], modiﬁed equations for the
strain rate of nanocrystalline material due to GB sliding were
derived. In the simulations, it was shown that dependence of
deformation rate on the grain size is stronger in the case of triple
junction diffusion controlled sliding than in the case when GBsliding is controlled by the GB diffusion. For example, decreasing
the average grain size by a factor of 2 increases the deformation
rate by a factor of 16. Further, the GB dislocation nucleation (e.g.,
Shockley partial dislocation) accompanied by atomic shufﬂes and
stress-assisted free volume migration at the GB was investigated
using the developed ‘‘toy model’’ of the GB sliding. With this model,
the typical mechanisms and feature of GB sliding were observed,
among others, macroscopic shear bands formation at the advanced
stages of deformation and the GBs migration due to violation of the
conditions of mechanical equilibrium between the GBs caused by
dislocations absorption/emission.
4.4. Phase transitions in nanostructured nitinol
With view on the enhancement of nitinol properties and
development of nanostructuring technologies for SMAs, the
development of methods for the property prediction based on
information about SMA microstructure and mechanical behavior is
of great importance. The crystallographic resource of the recovery
strain is determined by the maximum martensitic transformation
lattice strain. Two main methods are used for evaluating the
transformation lattice strain: calculations based on the phenome-
nological theory of martensitic transformation [138–140] and on
the deformation theory [141–143] . However, both methods are
based on certain assumptions: (1) a single crystal approach is
considered and (2) changes of martensite lattice parameters with
temperature [144–146] , composition [144,146] , and lattice distor-
tion in nanostructured material and texture formation are not
taken into consideration.
In Ref. [66], methods, algorithms and computer programs for
calculating the transformation lattice strain in single-crystal and
isotropic as well as textured polycrystalline SMA were developed.
The above calculations were applied to Ti–Ni and Ti–Nb–(Zr,Ta)
alloys.
Nitinol possesses the highest thermomechanical and super-
elastic properties as compared to other SMA [147–149] . However,
the presence of toxic nickel restricts its medical applications.
Therefore, there is a constant search for nickel-free SMA
compositions that can be used in the corrosive environment of
the human body. In this respect, Ti–Nb–Zr and Ti–Nb–Ta SMA
containing only biocompatible components seem to be the most
promising SMA [150–152] . These alloys are the objects for the
calculations and experimental validation together with Ti–Ni SMA.
4.4.1. Martensite lattice parameters and recovery strain in UFG Ti–Ni
and Ti–Nb-based alloys: phase transformation theory analysis
The structure evolution, martensitic transformations and
recovery strain of the NITI alloys, including ultraﬁne grained
nitinol, have been studied by using ﬁrst principle approaches
[153,154] , ﬁnite element models [163,164] (see also the next
section), and other methods. The micromechanical models seek to
include crystallographic, kinetic and microstructural aspects on
the phase transformation in SMA, using the continuum mechanics
methods [155–160] . Phenomenological models are based typically
on thermodynamics approach with macroscopic variables (see, e.g.
[161,162] .). Recently, Auricchio et al. [165,166] developed a 3D
phenomenological constitutive model for shape memory alloys
(SMAs), taking into account martensite reorientation and different
kinetics between forward/reverse phase transformations, low-
stress phase transformations as well as transformation-dependent
elastic properties. In Refs. [66,70–75] , a method and a computer
program for the precise calculation of martensite and austenite
lattice parameters from X-ray diffractograms data were developed
on the basis of the phenomenological theory of martensitic
transformations. This program can build a complete continuous
distribution of the stereographic projection of the transformationL. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 10

lattice strain which is a theoretical resource of the recovery strain
(Fig. 6). The martensite and austenite lattice parameters for Ti–Ni,
concentration and temperature dependencies of the maximum
transformation lattice strain for all crystallographic directions
were determined in an austenite single crystal approach for
tension and compression modes. This approach allows to
determine the crystallographic resource of the recovery strain,
orientation of the maximum recovery strain and maximum
transformation lattice strain values for Ti–Ni and Ti–Nb-(Zr,Ta)
SMA.
4.4.2. Thermomechanical modeling of martensitic transformation in
nanostructured and UFG nitinol: effect of grain sizes and their
distributions
The nanostructuring represents a promising way to improve the
reliability of parts from nitinol. The effect of the grain size on both
mechanical properties and martensitic transformations in NiTi
alloys has been studied in a number of investigations [167–175] .
So, Prokoﬁev et al. [168] demonstrated that the formation of UFG
(ultraﬁne grained) and NC (nanocrystalline) structures in nitinol
leads to the higher strength of the alloy, with narrow hysteresis
and low residual strain. Peterlechner et al. [169] observed
experimentally that the formation of the martensite is suppressed
with decreasing grain size. Burow et al. [170] investigated the
effect of various processing routes (ECAP, HPT, wire drawing + an-
nealing) of ultra-ﬁne grained (UFG) microstructures on martensitictransformations using the transmission electron microscopy and
differential scanning calorimetry. They observed that all UFG
materials show two-step transformations (as different from one-
step martensitic transformation on cooling in coarse grained
materials). It was also observed that UFG NiTi alloys show
strengthening effect and signiﬁcantly higher functional stability
during thermal cycling. Mei et al. [171] studied the nanostructured
NiTi with a graded surface nanostructure, and demonstrated that
the elastic modulus of nanostructured NiTi increases dramatically
with increasing the grain size. They explained it by the suppression
of stress-induced martensitic transformation in nanostructured
NiTi. In the works by the Austrian group [172–175] , mechanisms of
deformation of nanocrystalline NiTi were investigated using
various experimental (e.g., transmission electron microscopy
(TEM) and high resolution transmission electron microscopy
(HRTEM)) and theoretical methods. Karnthaler et al. [172] have
shown that severe plastic deformation of NiTi leads to amorphiza-
tion of the material, caused by plastic shear instability initiated at
shear bands. In their further investigations, Waitz et al. [173]
studied the effect of high pressure torsion (HPT) deformation on
the properties of nanocrystalline NiTi, and have shown that with
decreasing grain size, the energy barrier’’ for martensite transfor-
mation increases. The martensitic transformation is suppressed in
the materials with grains below 60 nm.
In order to determine the conditions and nanostructuring effect
on the shape memory effect numerically, the authors of [176]
Fig. 6. Crystallographic dependence of theoretical resource of shape recovery for Ti-50.0 at.% Ni SMA (in austenite single crystal).L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 11

simulated martensite phase transitions in nanocrystalline NiTi
using the ﬁnite element method and the thermodynamic theory
[177–180] . The ﬁnite element model of martensitic phase
transitions, based on the approach from [180] , includes the strain
softening due to martensitic phase transition and scale (grain size)
dependent material parameters. In the simulations, it was
demonstrated that the energy barrier for martensitic phase
transformation in nanocrystalline nitinol increase drastically with
decreasing the grain size [179] .
Further, it was observed in the FE simulations that the volume
content of martensitic phase decreases drastically with reducing
the grain size. When the grain size is smaller than some critical
value (around 50–80 nm, both in our simulations and in
experimental data), the martensitic phase transformations are
totally suppressed. On the basis of the comparison of graded and
localized distributions of grain sizes of nitinol with homogeneous
grain size distribution, it was observed that the martensite rich
regions form ﬁrst on the border between the coarse and ﬁne
grained regions, and expand inside the region with small grains
along the shear band direction. In the case of gradient micro-
structures, the effect is controlled not so by the relative gradient of
grain sizes, but rather by absolute grain sizes. In this case, the
nanostructured grains on the surface will probably prevent the
martensite formation (if they are below 50–80 nm), while the large
grains inside might undergo phase transitions if the high enough
stress is transferred to them.
In this section, the effect of nanostructuring on martensitic
phase transformations and mechanical properties of Ti–Ni SMA
was studied. It was concluded that the volume fraction of
martensitic phase decreases with reducing the grain size.
However, grain reﬁnement leads to signiﬁcant increase of
mechanical strength.
5. Biocompatibility and coatings for nanometal based implants
5.1. Biocompatibility of nanocrystalline Ti-based metals
5.1.1. Biocompatibility and corrosion behavior of Ti-based
nanomaterials
Nanocrystalline metals and alloys are characterized by their
extremely small grain sizes and correspondingly high volume
fraction of grain boundaries, which gives rise to unique physical,
chemical and mechanical properties compared with those of the
corresponding materials with conventional grain size. However,
the effect of nanostructuring on the corrosion behavior has not
been adequately studied. For metallic biomaterials, good corrosion
resistance is one of the major factors determining their biocom-
patibility. When metallic implants are placed in the electrolytic
environment of the human body, they become the site of
electrochemical reactions that lead to the release of metal ions
into the surrounding tissues and, in rare cases, to the loss of
implant functional ability. Pure Ti and Ti based alloys have
inherent corrosion resistance due to the spontaneous formation of
a passivating oxide layer. For pure Ti, the layer is a highly
protective Ti oxide and the only metal ions that can be released are
the ions of Ti. Although generally considered non-toxic, increased
concentrations of Ti ions have been shown to decrease the viability
of bone and other cells [181,182] . For Nitinol – a near-equiatomic
NiTi alloy, the presence of Ni ions in the passive Ti oxide layer
results in a less effective corrosion protection and correspondingly
lower biocompatibility. Of special concern is the release of Ni ions
due to their reported toxic, allergic, and potentially carcinogenic
effects [183,184] . Thus, despite a number of successful clinical
applications, the biocompatibility of Nitinol still remains contro-
versial [185–187] . The biocompatibility of porous NiTi proposed
for use as load bearing scaffolds [188–190] (i.e. the possible effectof NiTi corrosion products on various cells and living tissues) is
even more problematic. Given their high surface area and,
occasionally, crevice-like pore geometry, NiTi scaffolds can release
increased amounts of Ni ions that may cause allergic and
carcinogenic effects as well alter cell behavior [149] . Various
approaches, such as controlled oxidation [12,191,192] and
nitriding [193,194] were proposed to improve the biocompatibility
of Nitinol alloys and porous scaffolds.
Grain size decrease down to nanoscale can affect corrosion
behavior in several different ways. On the one hand, the high
density of intergranular surface defects could lead to a poor
corrosion performance since corrosion attack typically initiates at
surface heterogeneities. Since grain boundaries typically have a
higher energy than the interior of the grain; they will functions as
anodic sites. However, for nanocrystalline materials with their
extremely high volume fractions of grain boundaries, the atomic
compositional difference between the grain interior and the grain
boundary caused by atomic segregation can be strongly reduced.
This will result in a decrease in the potential difference between
the anodic and cathodic sites and lead to a low corrosion rate. For
alloys with elements that can form passive ﬁlms, the atoms of
these elements can diffuse easily along grain boundaries to the
surface of the alloy to form a protective passive layer. Such
preferential diffusion can result in a different (more solute-rich)
composition of the passive layer and correspondingly higher
corrosion resistance. Slightly lower corrosion rates were reported
for nanocrystalline Ti, as well as for electrodeposited nanocrystal-
line Co coatings compared to their microcrystalline counterparts
[150] ). The effect of nanocrystallization on the composition of the
passive ﬁlm has been reported for several alloys, including Fe–Cr
alloy [195] , stainless steel [196] and Ni-based superalloy [197] . For
all the nanocrystalline materials, the oxide ﬁlm was enriched in
elements with high afﬁnity for oxygen (Cr and Ti) resulting in
enhanced corrosion resistance. Improved corrosion behavior in
physiological solution was also reported for nanocrystalline Co–Cr
alloy [198] . At the same time, no improvement of corrosion
resistance was reported for nanocrystalline titanium [199] and Al–
Mg-based alloys [207] . Basing on the limited corrosion data
available in the literature for nanocrystalline alloys, it is impossible
to conclude how the corrosion behavior of nanocrystalline Ti and
TiNi alloys fabricated by severe plastic deformation will compare
with the corresponding conventional grain-size materials.
5.1.2. Molecular dynamics modeling of dissolution and ion diffusion
from the surface and GBs of Ti–Ni into body ﬂuid
The material dissolution and ion diffusion from the surface of
titanium-based materials are important factors of biocompatibility
of these materials. They were investigated by many authors [200–
206] . While in most investigations the passive behavior of Ni–Ti
alloys was observed (see e.g. [205] ), it is also important to
understand and to know the parameters and mechanisms of ion
diffusion of NiTi in general case. In Ref. [206] , the diffusion process
at the interface of nickel and titanium crystals was investigated by
performing molecular dynamics (MD) simulations at different
temperatures, namely 500, 600 and 700 K (Fig. 7). The diffusion of
nickel atoms on the surface of titanium crystal in the presence of
aqueous environment atop the nickel surface was studied as well.
MD simulations were carried out using MBN Explorer software
package [83]. As a result of simulations, it was found the height of
the diffusion energy barrier which is 0.501 eV and 0.544 eV for
nickel and titanium atoms, respectively. On the basis of the
dependence of the diffusion coefﬁcient on temperature, the
diffusion coefﬁcient at the temperatures close to the room
temperature was estimated. It is equal to 3.45 /C2 10/C08A˚2/ps and
1.44 /C2 10/C08A˚2/ps for nickel and titanium, respectively. It was
further found that after 300 ps at 800 K the nickel clusterL. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 12

disintegrates and nickel atoms intercalate under the ﬁrst layer of
titanium crystal. The extrapolation procedure allowed to evaluate
the diffusion coefﬁcient of nickel atoms at 310 K as 6.87 /C2 10/C04A˚2/
ps.
5.1.3. Experimental study of corrosion and ion release of
nanostructured NiTi in physiological solution
The corrosion and electrochemical behavior of nanocrystalline
and micron grain size Nitinol materials was studied in Ringer’s
solution which simulates physiological (body) ﬂuid. The concen-
tration of Ni and Ti ions in the withdrawn solution was measured
by Inductively Coupled Plasma Absorption Emission Spectroscopy
(ICP-AES).
For all the Nitinol specimens, the release of Ti ions was always
below the detection limit. Practically no Ni release (below or
slightly above the detection limit) was measured throughout the
experiment for both the coarse- and nanograin Ti49.8Ni50.2, as well
as for nano-Ti 49.4Ni50.6after HPT. All these specimens had a single-
phase austenitic (B2) microstructure, and SPD processing had no
effect on Ni ion release. In one group of Nitinol specimens,
however, relatively high amounts of Ni ions were released both
before and after SPD processing. Measurable Ni concentrations
were detected as early as 48 h immersion. According to X-ray
diffraction analysis, this material had a multi-phase composition,
the major phase being austenitic NiTi (B2), and the rest –
martensitic NiTi (B190) and Ti2Ni. In SEM, it was observed that
the material was highly non-homogeneous, with numerous
inclusions of Ti2Ni in the NiTi matrix, which must have led to
the low corrosion characteristics and high ion release. Again, no
effect of SPD processing on Ni ion release was observed. In each
Nitinol group (single- and multi-phase), the electrochemical
characteristics (corrosion, pitting and repassivation potentials)
of nanocrystalline alloys fabricated by ECAP and/or high pressure
torsion (HPT) were comparable to those of the corresponding
conventional grain size Nitinol.
Fig. 8 shows the cumulative Ni release from nano-Nitinol
produced by different SPD processes as compared to coarse-
grained Nitinol.
The results obtained show that the corrosion resistance and
metal ion release of nanocrystalline Nitinol materials is at least as
good as that of their conventional grain size counterparts. This is in
agreement with the results reported in Ref. [208] where ultraﬁne-
grained (200–300 nm) Ni50.8Ti49.2 prepared by ECAP technique
exhibited a corrosion behavior similar to that of the commercial
coarse-grained material. This means that nanocrystalline alloys are
biocompatible and can be used for human body implantation. At the
same time, to maintain adequate corrosion behavior of NiTi, it is
highly important that the microstructure is homogeneous, with no
second phase inclusions. Basing on the presented results, as well ason the limited literature data available, it was assumed that the high
volume fraction of grain boundaries in nanocrystalline Ti-based
alloys doesn’t lead to enhanced corrosion and dissolution, presum-
ably due to the highly passive nature of the titanium oxide surface
layer. Moreover, it is plausible that nanostructuring promotes the
formation of the Ti oxide ﬁlm, due to the high density and hence
availability of short-circuit diffusion paths. The structure and
chemical composition of the surface oxide (albeit only several to
tens of nanometers thick) are among the main factors determining
the corrosion behavior of biomedical Ti-based alloys. The effect of
enhanced transport along titanium nanograin boundaries on the
oxide characteristics requires further investigation.
5.2. Bioactive coatings and their effect on the mechanism of
deformation
5.2.1. Role of bioactive coatings in Ti-based implants
While the most important requirements to the permanent hard
tissue replacements are long term performance and stability, Ti has
poor tribological properties and tends to undergo severe wear,
making it unsuitable for articulating implant components. Host
response to wear debris has been implicated as the main cause of
aseptic loosening and premature failure of total joint replace-
ments.
Titanium is not bioactive and does not bond directly to the
bone, what can lead to small shifting and loosening of the implant.
Further, toxic and carcinogenic ions (like Ni from Ti–Ni and Al and
V from Ti–6Al-4V) can be in some cases released into the body
Fig. 8. Cumulative Ni release from nano-Nitinol produced by different SPD
processes as compared to coarse-grained Nitinol.
Fig. 7. Initial and ﬁnal structures of the Ni–Ti interface. Titanium and nickel atoms are shown by red and blue colors, respectively. (For interpretation of the references to color
in this ﬁgure legend, the reader is referred to the web version of the article.)L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 13

environment and may initiate long-term health problems, such as
Alzheimer disease, neuropathy and osteomalacia.
An effective way to promote the formation of a bone-like layer
on the implant surface, prevent toxic ion release, and improve
mechanical and tribological characteristics is the deposition of
multifunctional bioactive ﬁlm. Recently, a new approach to the
design of thin-ﬁlm biomaterials for medical applications has been
developed [210,211] . Multifunctional bioactive nanostructured
ﬁlms (MuBiNaFs) were deposited by magnetron sputtering of
composite targets based on nonstoichiometric titanium carbide
TiC 0.5with various inorganic additives (CaO, TiO 2, ZrO 2, Si3N4,
Ca3(PO 4)2, and Ca10(PO 4)6(OH) 2) [212,213] . Also microarc method
of applying coatings on the surface of metal implants is quite
technological and allows the formation of thick porous coating,
which promotes intensive ingrowth of bone tissue into the surface
of the implant [214,215] .
Multifunctional bioactive coatings accelerate the adaptation of
implants in human bodies and improve their performances.
Multifunctional bioactive nanostructured ﬁlms (MuBiNaFs) which
are deposited using magnetron sputtering of composite targets,
demonstrate high hardness, fatigue and adhesion strength,
reduced Young’s modulus, low wear and friction, high corrosion
resistance with high level of biocompatibility, bioactivity, and
biostability, and, thus, are promising candidates as protective ﬁlms
on the surface of metallic implants such as orthopedic prostheses,
materials for connective surgery and dental implants.
5.2.2. Deformation and strength of bioactive coatings
In Ref. [209] , mechanisms of deformation of multicomponent
bioactive nanostructured ﬁlms (MUBINAF) and protective wear
resistant TiN coatings on the substrate of various biocompatible Ti-
based nanomaterials (Ti, Ti-alloy with shape memory effect, and
Ti-alloy with superelasticity effect) were investigated under
mechanical loading expected in implants.
Analyzing the indents in uncoated samples using Scanning
Electron (SEM) and Scanning Probe (SPM) microscopy, one
observed only homogeneous deformation at indentation. In
contrast, the MUBINAF TiCaPCON/substrate system shows a very
speciﬁc mechanical behavior. The parameter H3/E2(hardness/
Young modulus ratio, which deﬁnes the mechanism of plastic
deformation in materials), determined for the TiCaPCON/substrate
systems, was varied from 0.32 (TiNi) to 0.4 (Ti) and to 0.55
(TiNbZr). Practically, it means the non-monotonic deformation
mechanisms and the formation of inhomogeneous mechanism
involving the formation of shear bands under indentation. Indeed,
a system of steps parallel to indent faces as well as cracks was
observed in the indents. In case of the coatings deposited on SMA
substrates (TiNi and TiNb-based), the appearance of shear bands is
less pronounced. It may be connected with pseudo elastic recovery
of the SMA substrates compared to that made of micro and
nanostructured pure titanium. In fact the depth of imprint is about
twice less for MUBINAF onto shape memory substrates (MDTNT2)than for MUBINAF onto ns-Ti (MDT3). It should be noted also that
steps on the proﬁle are larger at MDT3 system and more ﬁne for
MDTNT2 one.
It can be concluded that deposition of TiCaPCON coating not
only improves the mechanical properties (hardness, Young
modulus, elastic recovery) but also changes a mechanism of
localized deformation in the near-surface layers. Deformation was
found to proceed inhomogeneously, through formation of shear
bands during penetration of a Vickers diamond indenter. Forma-
tion of shear bands is most pronounced in case of substrates with
higher E and lower elastic recovery (R), such as ms-Ti (E = 125–
130 GPa, R = 10–12%). In the dynamic impact testing experiments,
the relationships between generally critical loads (loads, at which a
coating starts to fracture) and number of cycles were studied.
During these experiments all the samples (MUBINAF, deposited
onto micro- and nanostructured Ti-based substrates, namely Ti,
shape memory alloy Ti–Ni, Ti–Nb–Ta and Ti–Nb–Zr) were tested
for three different durations: 104, 5 /C2 104and 105cycles, to plot
the fatigue curves. It can be clearly seen that in case of Ti–Nb–Ta
and Ti–Nb–Zr substrates behavior and values of the MUBINAF
critical loads do not considerably depend on the substrate
structure and material. In contrast, MUBINAF, deposited onto Ti
and Ti–Ni substrates, exhibited an evident dependency on the
substrate structure. For example, MUBINAF critical loads for
nanostructured Ti–Ni substrates were 2.5 times higher than those
of microstructured ones for all numbers of impacts. The MUBINAF
on Ti showed different behaviors depend upon substrate material
structure, but overall the coating, deposited onto microstructured
substrate, performed better in the tests
5.2.3. Multilevel modeling of strength and failure of nanostructured
bioactive coatings on Ti-based biomaterials
The strength and failure of coatings on the Ti-based implants
are controlled by the mechanics of thin ﬁlm/ductile substrate
systems, as reviewed in Ref. [216] . The main mechanisms of
coating failure in this case (cracking, decohesion and delamina-
tion) are often modeled with the use of analytical fracture
mechanics based models, lattice network models, probabilistic
models of ﬂaw/crack distribution, stress distribution analysis,
which yields periodic stress distributions [216–222] . In Ref. [95], a
multilevel model based on the MCA (movable cellular automata
[223] ) is developed and applied for the computational analysis of
mechanical behavior of protective coatings (TiCaPCON) on
nanocrystalline Ti-based materials. The simulated cellular autom-
aton model is presented in Fig. 9 as fcc packing of automata.
Displacement, automata velocities, stress ﬁelds as well as the
force-indentation depth curves were obtained for different coating
thicknesses and substrate structures, and compared with experi-
ments. It was concluded that deposition of TiCaPCON coating not
only improves the mechanical properties (hardness, Young
modulus, elastic recovery) but also changes a mechanism of
localized deformation in the near-surface layers.
Fig. 9. Model for indentation represented by automata packing (a) and ﬁeld of automata velocities (b, m/s) as a section along the symmetry plane.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 14

Further, the coatings on nanostructured substrates were more
resistant to adhesive failures, than the ones on the substrates with
coarse-grained microstructure. The coating deposited onto nano-
structured Ti–Ni alloy substrate were found to possess the highest
adhesive/cohesive strength (27 N and 50 N, respectively), while
the lowest ones were for the coating deposited onto coarse-grained
titanium and Ti–Nb–Ta substrates.
Summarizing the studies, one can state that the coatings have a
great potential to improve strength, reliability and lifetime of
implants from nanostructured materials. Still, detailed studies are
necessary for each coating/substrate combinations to ensure the
optimal use of the potential.
5.3. Wear resistant TiN based PIRAC coatings on nanostructured Ti-
based alloys
Despite excellent biocompatibility and biomechanical proper-
ties, the use of Ti alloys in implantable devices is limited by their
strong susceptibility to abrasive and adhesive wear. Generation
and accumulation of wear debris between the sliding implant
surfaces or at implant/bone or implant/bone cement interfaces
may cause bone resorption jeopardizing the long-term stability of
the prosthesis. As a result of their inadequate wear behavior,
titanium alloys are not used, for example, as articulating
components in total joint replacements, but only as femoral
stems, acetabular shells and tibial trays [62,224,225] . The more
widespread use of Ti and its alloys in orthopedics, especially as
articulating TJR (total joint replacement) components, depends on
our ability to improve their wear resistance. Coating Ti alloy
implant components with a thin TiN layer is expected to provide
them with the required high wear resistance [226,227] . TiN-coated
Ti alloy parts are offered as substitutes to the traditional CoCr alloy
components in both knee and hip systems for nickel-sensitive
patients or where large-diameter femoral heads are indicated
(heavy, active patients). A number of techniques can be used for
the fabrication of hard TiN coatings, the most commonly used
being physical vapor deposition – PVD [226–229] . As the low-
temperature PVD process does not generally involve diffusion
phenomena and chemical reactions, the adhesion between the
substrate and the hard layer is weak. The adhesion is further
compromised by high residual stresses associated with ceramic
PVD coatings on metal substrates [230] . As a result, delamination
and spallation of TiN-PVD coatings from the articulating surfaces of
orthopedic implants was observed in in vitro wear simulations, in
animal tests and in clinical trials [228,231] . To prevent the failure
of TiN coating adhesion, surface modiﬁcation methods capable of
producing a strong TiN coating-substrate interface should be
looked for. A new reactive diffusion process called PIRAC (Powder
Immersion Reaction Assisted Coating) nitriding has been proposed
as an attractive alternative to conventional PVD-based nitriding
techniques. In PIRAC, a several micron thick TiN coating is formed
by interaction of Ti-based substrate with highly reactive mon-
atomic nitrogen supplied by decomposition of an unstable nitride
and/or by selective diffusion of the atmospheric nitrogen. Reactive
diffusion of nitrogen atoms into titanium alloy results in the
formation of a Ti–N coating. PIRAC nitrided Ti surface consists of a
several micrometers thick outer compound layer (TiN–Ti 2N) and a
several tens of microns thick inner solid solution layer. Beneath the
ceramic, a nitrogen-enriched Ti gradually transforms into the
metal alloy, preventing an abrupt mismatch in properties. This
hardened N-rich titanium layer provides an optimal support for the
ceramic coating and prevents its collapse and delamination. The
low level of residual stresses in PIRAC coatings on Ti-6Al-4V
substrate compared to the PVD TiN layers is an additional factor in
the excellent adhesion of PIRAC coatings. In contrast to PVD, PIRAC
coatings are not externally applied layers but are grown from thesubstrate itself and are characterized by an excellent conformity
and strong adhesion [232,233] . As PIRAC is not a line-of-sight
process, it allows uniform coating of complex shape implant
components. TiN PIRAC coated Ti–6Al–4V and NiTi exhibited
excellent corrosion resistance reduced metal ion release [193,234] .
Moreover, good biocompatibility of TiN PIRAC coated Ti–6Al–4V
alloy with both soft and bone tissues was reported in Ref. [235] .
However, TiN-PIRAC coatings are typically produced at relatively
high temperatures that can cause the coarsening of nanocrystalline
structure. Indeed, some coarsening of micron-scale Ti alloy grains
was observed after long (192 h) PIRAC nitriding treatments at
700 8C [236] . So, the question arises whether such TiN based PIRAC
coatings can be used for protection of nanocrystalline Ti-based
implants.
In order to explore the possibility of nanostructure retention in
pure Ti and NiTi (nitinol) alloy, relatively short (up to 2 h) PIRAC
nitriding treatments of ECAP-processes materials were performed
at 600 and 650 8C. As demonstrated by X-ray diffraction analysis
(see Fig. 10), titanium nitride (TiN–T 2N) based hard coatings were
formed on both nanostructured Ti and nitinol. The coatings
obtained were approximately 0.3 mm thick, which could be
enough to provide good wear resistance. High resolution SEM
examination revealed that practically no growth of 100–150 nm
nanograins occurred after 100 h exposure of pure Ti at 600 8C and
of Nitinol at 650 8C (see Fig. 11). Thus, TiN based reactive diffusion
coatings can be grown on nano-Ti and nano-NiTi by PIRAC nitriding
at low temperatures while retaining their initial ultraﬁne
nanostructure.
6. Potential for application: nanotitanium based implants with
small radius
The development of the technology of ECAP producing of UFG
titanium with enhanced mechanical properties made it possible to
produce dental implants with lower radii. According to the results
of the computational analysis, these low radius implants with a
diameter of 2.4 mm (Fig. 12) can withstand loads similar to those
carried by the implants of conventional design with a diameter of
3.5 mm made from coarse-grained Ti.
Rods of high strength nanostructured Ti (Grade-4) produced by
ECAP-C processed followed by drawing were subjected to grinding,
in order to produce the required surface quality and tolerance.
Cylindrical screw implants with the thread Timplant Nanoimplant
and a diameter of 2.4 mm and a length of the intraosseal part 10, 12
and 14 mm were manufactured from UFG Ti. The implant has a
polished gingival part with a cone top above it. The developed
implant is made from pure Ti and, therefore, it does not contain any
Fig. 10. XRD pattern of nano-Ti after PIRAC nitriding at 600 8C, 24 h.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 15

toxic alloying elements (like V) and elements classiﬁed as allergens
(like Ni, Co, or Cr). Another positive side of the low radius implant is
that it allows one to minimize medical intrusion, thus, making the
implants better bearable. These implants from nTi showed also
better biological properties than coarse grained Ti. The healing
process is faster and about 70% of nanoimplants could be loaded
immediate after inserting.
Further, another implant prototype with diameter of 2.0 mm
was developed in the framework of VINAT project. The implant
was manufactured from new UFG Ti with increased strength (U.T.S.
1330 MPa). The implant prototype was installed into body of a
patient. In the speciﬁc situation, the patient (18 years old, with no
space for bigger implant) in his mouth, was offered to install the
low radius implant (2.0 mm) (between teeth 11 and 13). Anotherimplant with the diameter of 2.4 mm was inserted to the right side
position 12. The man left the dental ofﬁce with two nanoimplants
and with two provisional crowns made in the same day as implants
were inserted (Fig. 12b and c). After 6 weeks, ﬁnal metalceramic
crowns were ﬁxed on the implants.
Other medical devices developed on the basis of the above
studies are a removable clip for clipping blood vessels based on
One-Way and Two-Way Shape Memory Effects, while another one
is an extractor ‘‘Trawl’’ for concernment removal based on
Superelasticity Effect. Their Ti–Ni working elements are made
from the thermomechanically treated Ti-50.7 at.% Ni SMA with
nanosubgrained structure. The devices had been created and
patented in a collaboration between MISIS and ‘‘Globetek 2000 Pty
Ltd.’’ (Australia). The clinical experiments are currently underway.
Fig. 11. Representative microstructures of nano-Ti: (a) as-produced by ECAP; (b) after PIRAC nitriding at 600 8C for 100 h. High-resolution SEM.
Fig. 12. Implant from nanostructured Ti (a) and (b) and (c) X-ray photos after surgery and control photo after incorporation of implants.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 16

7. Summary and conclusions
In this review, the application, fabrication, modeling and
development of ultraﬁne grained titanium based materials for
implantable devices and other medical applications are discussed.
The usability of different materials for surgical implants, nanos-
tructuring technologies for Ti-based materials, methods of
computational modeling and virtual testing of these materials
and reserves of their optimization are reviewed. Some recently
developed technologies of fabrication of nanostructured, high
strength, biocompatible materials for medical implants are out-
lined, among them, a novel thermomechanical processing route for
fabrication of nano-Ti with very homogeneous structure and
superior properties and thermomechanical treatment of nitinol.
Computational models and tools, developed for the simulation
and analysis of ultraﬁne grained Ti-based materials at different
scale levels, are reviewed. These models and tools can be applied to
the analysis of peculiarities of the structures of ultraﬁne grained
and nanocrystalline materials and special reserves of their
improvement. Among these effects, the effects of orientation
distribution, textures, non-equilibrium grain boundaries, diffusion
coefﬁcients and precipitates on the deformation behavior, grain
subdivision and interaction between grain boundary sliding,
diffusion and dislocation nucleation can be mentioned. These
models and studies should serve as a basis for further improve-
ment of UFG materials and technologies.
Bioactive coatings on nanocrystalline Ti-based implants are the
effective way to promote the formation of a bone-like layer on the
implant surface, prevent toxic ion release.
An example of successful development and installation of a
prototype, nanomaterial-based dental implant with lower radius
which can withstand loads similar to those carried by the implants
of conventional design, is presented.
Acknowledgement
The authors gratefully acknowledge the ﬁnancial support of the
Commission of the European Communities through the 7th
Framework Programme Grant ‘‘Virtual Nanotitanium’’ (VINAT,
Contract No. 295322) and ﬁnancial support of the Ministry of
Education and Science of the Russian Federation. L.M. and E.L.
acknowledge also the ﬁnancial support of the Ministry of
Education and Science of the Russian Federation in the framework
of Increase Competitiveness Program of NSTU MISIS,. I.S. acknowl-
edges Spanish Ministry of Economy and Competitiveness for
funding through the Ramon y Cajal Fellowship.
References
[1] Biocompatible Materials, US Industry Study with Forecasts to 2010 & 2015,
Study #2111, The Freedonia Group, September 2006, p. 264.
[2] D.H. Kohn, Curr. Opin. Solid State Mater. Sci. 3 (1998) 309–316.
[3] I. Gotman, J. Endourol. 11 (1997) 383–389.
[4] N. Soumya, R. Banerjee, in: R. Narayan (Ed.), ASM Handbook, vol. 23 ‘‘Materials
for Medical Devices’’, ASM International, Materials Park, OH, USA, 2012, pp. 6–17.
[5] M. Niinomi, Mater. Trans. 49 (2008) 2170–2178.
[6] M. Geetha, A.K. Singh, R. Asokamani, A.K. Gogia, Prog. Mater. Sci. 54 (2009) 397–
425.
[7] M. Long, H.J. Rack, Biomaterials 19 (1998) 1621–1639.
[8] M. Browne, P.J. Gregson, Biomaterials 21 (2000) 385–392.
[9] D. Zaffe, C. Bertoldi, U. Consolo, Biomaterials 25 (2004) 3837–3844.
[10] N.J. Hallab, S. Anderson, M. Caicedo, A. Brasher, K. Mikecz, J.J. Jacobs, J. Biomed.
Mater. Res. A 74 (2005) 124–140.
[11] N. Diomidis, S. Mischler, N.S. More, M. Roy, Acta Biomater. 8 (2012) 852–859.
[12] M. Niinomi, Metal. Mater. Trans. A 33 (2002) 477–486.
[13] R.Z. Valiev, Nat. Mater. 3 (2004) 511–516.
[14] I.A. Ovid’ko, T.G. Langdon, Rev. Adv. Mater. Sci. 30 (2012) 103–111.
[15] Y. Estrin, E.P. Ivanova, A. Michalska, V.K. Truong, R. Lapovok, R. Boyd, Acta
Biomater. 7 (2011) 900–906.
[16] T.N. Kim, A. Balakrishnan, B.C. Lee, W.S. Kim, B. Dvorankova, K. Smetana, et al. J.
Mater. Sci.: Mater. Med. 19 (2008) 553.[17] T. Duerig, A. Pelton, D. Sto¨ckel, Mater. Sci. Eng. A 273–275 (1999) 149–160.
[18] S.A. Shabalovskaya, Int. Mater. Rev. 46 (2001) 1–18.
[19] C.D.J. Barras, K.A. Myers, Eur. J. Vasc. Endovasc. Surg. 19 (2000) 564–569.
[20] S. Shabalovskaya, J. Anderegg, J. Van Humbeeck, Acta Biomater. 4 (2008) 447–
467.
[21] A. Michiardi, C. Aparicio, J.A. Planell, J.F. Gil, J. Biomed. Mater. Res. B 77 (2006)
249–256.
[22] R.Z. Valiev, D. Gunderov, E. Prokoﬁev, V. Pushin, Y.T. Zhu, Mater. Trans. 49 (2008)
97–101.
[23] V. Brailovski, S. Prokoshkin, I. Khmelevskaya, K. Inaekyan, V. Demers, S. Dobat-
kin, E. Tatyanin, Mater. Trans. 47 (2006) 795–904.
[24] S. Prokoshkin, V. Brailovski, K. Inaekyan, V. Demers, I. Khmelevskaya, S. Dobat-
kin, E. Tatyanin, Mater. Sci. Eng. A 481482 (2008) 114–118.
[25] I.Y. Khmelevskaya, S.D. Prokoshkin, V. Dobatkin, E.V. Tatyanin, I.B. Trubitsyna,
Mater. Sci. Eng. A 438–440 (2006) 472–475.
[26] R.Z. Valiev, I. Sabirov, A.P. Zhilyaev, T.G. Langdon, JOM 64 (2012) 1134–1142.
[27] R.Z. Valiev, I.P. Semenova, V.V. Latysh, H. Rack, T.C. Lowe, J. Petruzelka, L. Dluhos,
D. Hrusak, J. Sochova, Adv. Eng. Mater. 10 (2008) B15–B17.
[28] L. Mishnaevsky, Jr., E. Levashov (Eds.), Selected Publications of the EU FP7 project
Virtual Nanotitanium (VINAT) ‘‘Theoretical analysis and virtual testing of tita-
nium-based nanomaterials’’, Comp. Mater. Sci., vol. 76, 2013, pp. 1–2.
[29] R.Z. Valiev, T.G. Langdon, Prog. Mater. Sci. 51 (2006) 881–981.
[30] G.J. Raab, R.Z. Valiev, T.C. Lowe, Y.T. Zhu, Mater. Sci. Eng. A 382 (2004) 30–34.
[31] A. Rosochowski, L. Olejnik, J. Mater. Process. Technol. 125–126 (2002) 309–316.
[32] A.P. Zhilyaev, T.G. Langdon, Prog. Mater. Sci. 53 (2008) 893–979.
[33] Y. Saito, H. Utsunomiya, T. Sakai, R.G. Hong, Scr. Mater. 39 (1998) 1221–1227.
[34] M. Lewandowska, K.J. Kurzydlowski, J. Mater. Sci. 43 (2008) 7299–7306.
[35] Y. Estrin, A. Vinogradov, Acta Mater. 61 (2013) 782–817.
[36] B. Verlinden, Metalurgija 11 (3) (2005) 165–182.
[37] R.Z. Valiev, R.K. Islamgaliev, I.V. Alexandrov, Prog. Mater. Sci. 45 (2000) 103–189.
[38] V.V. Stolyarov, Y.T. Zhu, I.V. Alexandrov, T.C. Lowe, R.Z. Valiev, Inﬂuence of ECAP
routes on the microstructure and properties of pure Ti, Mater. Sci. Eng. A 299
(2001) 59–67.
[39] I. Sabirov, R.Z. Valiev, I.P. Semenova, R. Pippan, Metall. Mater. Trans. A 41 (2010)
727–733.
[40] V.L. Sordi, M. Ferrante, M. Kawasaki, T.G. Langdon, J. Mater. Sci. 47 (2012) 7870–
7876.
[41] J. Gubicza, Zs. Fogarassy, Gy. Kra´llics, J. La´ba´r, T. To¨rko¨ly, Mater. Sci. Forum 589
(2008) 99–104.
[42] D.V. Gunderov, A.V. Polyakov, I.P. Semenova, G.I. Raab, A.A. Churakova, E.I.
Gimaltdinova, I. Sabirov, J. Segurado, V.D. Sitdikov, I.V. Alexandrov, N.A. Enikeev,
R.Z. Valiev, Mater. Sci. Eng. A 562 (2013) 128–136.
[43] A.V. Sergueeva, V.V. Stolyarov, R.Z. Valiev, A.K. Mukherjee, Scr. Mater. 45 (2001)
747–752.
[44] I.P. Semenova, E.B. Yakushina, V.N. Nurgaleeva, R.Z. Valiev, J. Mater. Sci. 100
(2009) 1691–1696.
[45] S. Zherebtsov, G. Salishchev, R. Galeyev, K. Maekawa, Mater. Trans. 46 (2005)
2020–2025.
[46] J. Ma, I. Karaman, B. Kockar, H.J. Maier, Y.I. Chumlyakov, Mater. Sci. Eng. A 528
(2011) 7628–7635.
[47] R.Z. Valiev, D.V. Gunderov, V.G. Pushin, J. Metastable Nanocryst. Mater. 24–25
(2005) 7–12.
[48] I. Sabirov, M.T. Perez-Prado, J.M. Molina-Aldareguia, I.P. Semenova, G.Kh. Sal-
imgareeva, R.Z. Valiev, Scr. Mater. 64 (2011) 69–72.
[49] M. Niinomi, Mater. Sci. Eng. A 243 (1998) 231–236.
[50] V.G. Pushin, R.Z. Valiev, Y.T. Zhu, S.D. Prokoshkin, D.V. Gunderov, L.I. Yurchenko,
Mater. Sci. Forum 503–504 (2006) 539–544.
[51] V.V. Stolyarov, E.A. Prokoﬁev, S.D. Prokoshkin, S.V. Dobatkin, I.B. Trubitsyna, I.Yu.
Khmelevskaya, V.G. Pushin, R.Z. Valiev, Phys. Met. Metall. 100 (2005) 608–618.
[52] S.D. Prokoshkin, I.Y. Khmelevskaya, S.V. Dobatkin, I.B. Trubitsyna, E.V. Tatyanin,
V.V. Stolyarov, E.A. Prokoﬁev, Acta Mater. 53 (2005) 2703–2714.
[53] V.G. Pushin, V.V. Stolyarov, R.Z. Valiev, T.C. Lowe, Y.T. Zhu, Mater. Sci. Eng. A 410–
411 (2005) 386–389.
[54] A.V. Sergueeva, C. Song, R.Z. Valiev, A.K. Mukherjee, Mater. Sci. Eng. A 339 (2003)
159–165.
[55] Th. Waitz, C. Tecn. Mat. 20 (2008) 25–29.
[56] E.Y. Gutmanas, A. Rabinkin, M. Roitberg, Scr. Metall. 13 (1979) 11–15.
[57] E.Y. Gutmanas, Powder Metall. Int. 15 (1983) 129–132.
[58] E.Y. Gutmanas, ASM Handbook, vol. 7, ‘‘Powder Metal Technologies and
Applications’’, ASM International, Materials Park, OH, 1998, pp. 574–582.
[59] E.Y. Gutmanas, L.K. Trusov, I. Gotman, Nanostruct. Mater. 4 (1994) 893–901.
[60] E.Y. Gutmanas, A. Trudler, I. Gotman, J. Metastable Nanocryst. Mater. 386–388
(2002) 329–334.
[61] E.Y. Gutmanas, I. Gotman, L. Farber, E. Paransky, Proc. Powder Metallurgy World
Congress, Kyoto, Japan, (1993), pp. 1148–1151.
[62] E.Y. Gutmanas, Prog. Mater. Sci. 34 (1990) 261–366.
[63] I.V. Alexandrov, R.G. Chembarisova, Rev. Adv. Mater. Sci. 16 (2007) 51–72.
[64] H.S. Kim, Yu. Estrin, Mater. Sci. Eng. A 410–411 (2005) 285–289.
[65] H. Petryk, S. Stupkiewicz, Int. J. Mater. Res. 103 (2012) 3.
[66] L. Mishnaevsky Jr., et al., Theoretical analysis, design and virtual testing of
biocompatibility and mechanical properties of titanium-based nanomaterials,
EP FP7 VINAT Project Periodic Report, DTU, Roskilde, 2012p. 128.
[67] M.G.C. Seefeldt, Comp. Mater. Sci. 76 (2013) 12–19.
[68] J. Segurado, J. Llorca, Comp. Mater. Sci. 76 (2013) 3–11.
[69] V. Brailovski, S. Prokoshkin, K. Inaekyan, V. Demers, Proc. 8th European Sympo-
sium on Martensitic Transformations ESOMAT 2009, 07–11 Septermber 2009,L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 17

EDP Sciences, Prague, 2009, pp. 1–10 , http://dx.doi.org/10.1051/esomat/
200901001 .
[70] S.D. Prokoshkin, Y. Khmelevskaya, S.V. Dobatkin, I.B. Trubitsyna, E.V. Tatyanin,
V.V. Stolyarov, E.A. Prokoﬁev, Acta Mater. 53 (2005) 2703–2714.
[71] V. Brailovski, S. Prokoshkin, P. Terriault, F. Trochu (Eds.), Shape Memory Alloys:
Fundamentals, Modeling and Applications, ETS Publ., Montreal, 2003, , 851 p..
[72] V. Brailovski, S. Prokoshkin, I. Khmelevskaya, K. Inaekyan, V. Demers, S. Dobat-
kin, E. Tatyanin, Mater. Trans. 47 (2006) 795–804.
[73] S. Prokoshkin, V. Brailovski, K. Inaekyan, V. Demers, I. Khmelevskaya, S. Dobat-
kin, E. Tatyanin, Mater. Sci. Eng. A 481–482 (2008) 114–118.
[74] V. Brailovski, S. Prokoshkin, K. Inaekyan, V. Demers, J. Alloys Compd. 509 (2011)
2066–2075.
[75] S.D. Prokoshkin, V. Brailovski, A.V. Korotitskiy, K.E. Inaekyan, A.M. Glezer, Phys.
Metal. Metall. 110 (2010) 289–303.
[76] J. Li, G.J. Weng, Int. J. Plast. 23 (2007) 2115–2133.
[77] P. Barai, G.J. Weng, Acta Mech. 195 (2008) 327–348.
[78] E. Gu¨rses, T. El Sayed, Mater. Lett. 65 (2011) 3391–3395.
[79] W. Yang, H. Wang, J. Mech. Phys. Solids 52 (2004) 875–879.
[80] B. Zhu, R.J. Asaro, P. Krysl, R. Bailey, Acta Mater. 53 (2005) 4825–4838.
[81] R.J. Asaro, P. Krysl, B. Kad, Phil. Mag. Lett. 83 (2003) 733–743.
[82] S. Hao, B. Moran, W.K. Liu, G.B. Olson, J. Comput. Aided Mater. 10 (2003) 99–142.
[83] I.A. Solov’yov, P.V. Nikolaev, A.V. Yakubovich, V.V. Dick, A.V. Solov’yov, MBN
Explorer Users’s Guide, Version 1.0.0, FIAS Preprint, 2010 244 pp..
[84] K. Saitoh, K. Kubota, T. Sato, Technische Mechanik 30 (2010) 269–279.
[85] G.J. Ackland, A.P. Jones, R. Noble-Eddy, Mater. Sci. Eng. A 481–482 (2008) 11.
[86] T. Sato, K. Saitoh, N. Shinke, Model. Simulat. Mater. Sci. 14 (2006) S39–S46;
T. Sato, K. Saitoh, N. Shinke, Mater. Sci. Eng. A 481–482 (2008) 250–253.
[87] D. Farkas, D. Roqueta, A. Viette, K. Ternes, Model. Simulat. Mater. Sci. Eng. 4
(1996) 359–369.
[88] M.I. Baskes, Phys. Rev. B. 46 (1992) 2727–2742;
Y.-M. Kim, B.-J. Lee, M.I. Baskes, M.I. Baskes, Phys. Rev. B 74 (2006) 014101:1–
014101:12.
[89] W.S. Lai, B.X. Liu, J. Phys.: Condens. Mater. 12 (2000) L53.
[90] H. Tsuzuki, P.S. Branicio, J.P. Rino, Comput. Phys. Commun. 177 (2007) 518.
[91] K. Kadau, T.C. Germann, P.S. Lomdahl, B.L. Holian, D. Kadau, P. Entel, M. Kreth, F.
Westerhoff, D.E. Wolf, Metall. Mater. Trans. A 35 (2004) 2719–2722.
[92] X. Huang, K.M. Rabe, G.J. Ackland, Nat. Mater. 2 (2003) 307–311.
[93] X. Huang, K.M. Rabe, G.J. Ackland, Phys. Rev. B 67 (2003) 024101.
[94] G.B. Sushko, A.V. Verkhovtsev, A.V. Yakubovich, A.V. Solov’yov, J. Phys.: Conf. Ser.
438 (2013) 012021-1–012021-11.
[95] S.G. Psakhie, A.Yu. Smolin, E.V. Shilko, G.M. Anikeeva, Yu.S. Pogozhev, M.I.
Petrzhik, E.A. Levashov, Comp. Mater. Sci. 76 (2013) 89–98.
[96] H. Van Swygenhoven, A. Caro, D. Farkas, Mater. Sci. Eng. A 309–310 (2001) 440–444;
P.M. Derlet, H. Van Swygenhoven, Scripta Mater. 47 (2002) 719–724.
[97] V. Yamakov, S.R. Phillpot, D. Wolf, H. Gleiter, Acta Mater. 50 (2002) 5005–5020.
[98] S. Li, et al. Comp. Mater. Sci. 45 (2009) 390–397.
[99] J.E. Carsley, J. Ning, W.W. Milligan, S.A. Hackney, E.C. Aifantis, Nanostruct. Mater.
5 (1995) 441–448.
[100] L. Mishnaevsky Jr., Computational Mesomechanics of Composites, John Wiley,
London, 2007p. 280.
[101] L. Mishnaevsky Jr., Rev. Adv. Mater. Sci. 30 (2012) 60–72.
[102] H.S. Kim, Scr. Mater. 39 (1998) 1057–1061.
[103] H.S. Kim, C. Suryanarayana, S.J. Kim, B.S. Chun, Powder Metall. 41 (1998) 217–
220.
[104] A. Hasnaoui, H.V. Swygenhoven, P.M. Derlet, Acta Mater. 50 (2002) 3927–3939.
[105] G.J. Tucker, D.L. McDowell, Int. J. Plast. 27 (2011) 841–857.
[106] V.N. Chuvil’deev, Non-equilibrium grain boundary in metals, Theory and
applications, Fizmatlit, Moscow, 2004.
[107] V.N. Chuvil’deev, V.I. Kopylov, W. Zeiger, Ann. Chim. Sci. Mat. 27 (2002) 55–64.
[108] H.S. Liu, W. Pantleon, L. Mishnaevsky Jr., Comp. Mater. Sci. 83 (2014) 318–330.
[109] H.S. Liu, L. Mishnaevsky Jr., Acta Mater. (2014) , http://dx.doi.org/10.1016/
j.actamat.2014.03.017 .
[110] Y. Amouyal, E. Rabkin, Acta Mater. 55 (2007) 6681–6689.
[111] G.I. Taylor, J. Inst. Met. 62 (1938) 307–324.
[112] R. Hill, J. Mech. Phys. Solids 14 (1966) 95–102.
[113] R. Hill, J. Rice, J. Mech. Phys. Solids 20 (1972) 401–413.
[114] R. Asaro, Advances in Applied Mechanics, vol. 23, Academic Press, New York,
1983.
[115] D. Pierce, R. Asaro, A. Needleman, Acta Metall. 30 (1982) 1087–1119.
[116] J.L. Bassani, T.Y. Wu, Proc. R. Soc. Lond. A 435 (1989) 21–41.
[117] F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, D. Raabe, Acta
Mater. 58 (2010) 1152–1211.
[118] J.F. Nye, Acta Metall. 1 (1953) 153–162.
[119] M.F. Ashby, Phil. Mag. 21 (1970) 399–424.
[120] E.C. Aifantis, J. Eng. Mater. Technol. 106 (1984) 326–330.
[121] N.A. Fleck, J.W. Hutchinson, Adv. Appl. Mech. 33 (1997) 295–361.
[122] N.A. Fleck, J.W. Hutchinson, J. Mech. Phys. Solids 49 (2001) 2245–2271.
[123] W.D. Nix, H. Gao, J. Mech. Phys. Solids 46 (1998) 411–425.
[124] M.E. Gurtin, Int. J. Plast. 26 (2010) 1073–1096.
[125] L. Bardella, J. Mech. Phys. Solids 54 (2006) 128–160.
[126] A.A. Fedorov, M.Yu. Gutkin, I.A. Ovid’ko, Scr. Mater. 47 (2002) 51–55.
[127] S.V. Bobylev, N.F. Morozov, I.A. Ovid’ko, Phys. Rev. Lett. 105 (2010) 055504.
[128] H. Van Swygenhoven, P.M. Derlet, Phys. Rev. B 64 (2001) 224105.
[129] H. Van Swygenhoven, P.M. Derlet, A. Hasnaoui, Phys. Rev. B 66 (2002) 024101.
[130] M. Ke, S.A. Hackney, W.W. Milliga, E.C. Aifantis, Nanostruct. Mater. 5 (1995)
689–697.[131] A. Haque, M.T.A. Saif, Deformation mechanisms in free-standing nanoscale thin
ﬁlms: a quantitative in situ transmission electron microscope study, Proc. Natl.
Acad. Sci. U.S.A. 101 (2004) 6335–6340.
[132] N.Q. Chinh, G. Vo¨ro¨s, P. Szommer, Z. Horita, T.G. Langdon, Adv. Mater. 18 (2006)
34–39.
[133] H. Van Swygenhoven, M. Spaczer, A. Caro, D. Farkas, Phys. Rev. B 60 (1999) 22–25.
[134] V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, H. Gleiter, Nat. Mater. 3
(2004) 43–47.
[135] M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater. Sci. 51 (2006) 427–556.
[136] R. Raj, M.F. Ashby, Metall. Trans. A 2 (1971) 1113–1127.
[137] M.R. Chellali, Z. Balogh, L. Zheng, G. Schmitz, Scr. Mater. 65 (2011) 343–346.
[138] S. Miyazaki, S. Kimura, K. Otsuka, Y. Suzuki, Scr. Metall. 18 (1984) 883–888.
[139] T. Saburi, M. Yoshida, S. Nenno, Scr. Metall. 18 (1984) 363–368.
[140] T. Saburi, in: K. Otsuka, C.M. Wayman (Eds.), Shape Memory Materials, Cam-
bridge Univ. Press, Cambridge, 1998, p. 57.
[141] L.A. Monasevich (Ed.), Shape Memory Alloys and Their Applications in Medicine,
Nauka, Novosibirsk, 1992, , 741 p..
[142] S.D. Prokoshkin, A.V. Korotitskiy, V. Brailovski, S. Turenne, I.Y. Khmelevskaya, I.V.
Trubitsyna, Acta Mater. 52 (2004) 4479–4492.
[143] S. Prokoshkin, A. Korotitskiy, A. Tamonov, I. Khmelevskaya, V. Brailovski, S.
Turenne, Mater. Sci. Eng. A 438–440 (2006) 549–552.
[144] S.D. Prokoshkin, V. Brailovski, S. Turenne, I.Y. Khmelevskaya, A.V. Korotitskiy, I.B.
Trubitsyna, J. Phys. IV 112 (2003) 651–654.
[145] Yu.P. Mironov, S.N. Kulkov, Izvestiya VUZov. Fizika 37 (1994) 49–54.
[146] S.D. Prokoshkin, V. Brailovski, K. Inaekyan, V. Demers, I. Khmelevskaya, S.
Dobatkin, E. Tatyanin, Mater. Sci. Eng. A 481–482 (2008) 114–118.
[147] H. Funakubo (Ed.), Shape Memory Alloys, Gordon and Breach Sci. Publ., N.Y.,
1975, , 275 p..
[148] K. Otsuka, C.M. Wayman (Eds.), Shape Memory Materials, Cambridge Univ.
Press, Cambrigde, 1998, , 284 p..
[149] V. Brailovski, S. Prokoshkin, P. Terriault, F. Trochu (Eds.), Shape Memory Alloys:
Fundamentals, Modeling and Applications, ETS Publ., Montreal, 2003, , 851 p;
J. Ryhanen, et al. J. Biomed. Mater. Res. 35 (1997) 451–457.
[150] S. Miyazaki, H.Y. Kim, H. Hosoda, Mater. Sci. Eng. A 438–440 (2006) 18–24.
[151] J.I. Kim, H.Y. Kim, T. Inamura, H. Hosoda, S. Miyazaki, Mater. Sci. Eng. A 403
(2005) 334–339.
[152] V. Brailovski, S. Prokoshkin, M. Gauthier, K. Inaekyan, S. Dubinskiy, M. Petrzhik,
M. Filonov, Mater. Sci. Eng. C 31 (2011) 643–657.
[153] M.F.-X. Wagner, W. Windl, Acta Mater. 56 (2008) 6232–6245.
[154] Z.-Y. Zeng, C.-E. Hu, L.-C. Cai, X.-R. Chen, F.-Q. Jing, Phys. B: Condens. Matter 405
(2010) 3665–3672.
[155] Q.P. Sun, K.C. Hwang, J. Mech. Phys. Solids 41 (1993) 1–17.
[156] B.C. Goo, C. Lexcellent, Acta Mater. 45 (1997) 727–737.
[157] X. Gao, M. Huang, L.C. Brinson, Int. J. Plast. 16 (2000) 1345–1369.
[158] X. Peng, W. Pi, J. Fan, Int. J. Plast. 24 (2008) 966–990.
[159] V.I. Levitas, I.B. Ozsoy, Int. J. Plast. 25 (2009) 239–280.
[160] X.M. Wang, B.X. Xu, Z.F. Yue, Int. J. Plast. 24 (2008) 1307–1332.
[161] L.C. Brinson, J. Intel. Mater. Syst. Struct. 4 (1993) 229–242.
[162] J.G. Boyd, D.C. Lagoudas, Int. J. Plast. 12 (1996) 805–842.
[163] J. Gemperlova, V. Paidar, F. Kroupa, Czech. J. Phys. 39 (1989) 427–446.
[164] C. Grossmann, A. Schaefer, M.F.-X. Wagner, Mater. Sci. Eng. A (2009) 1172–1178.
[165] F. Auricchio, R.L. Taylor, J. Lubliner, Comput. Methods Appl. Mech. Eng. 146 (3–4)
(1997) 281–312.
[166] F. Auricchio, E. Bonetti, G. Scalet, F. Ubertinic, Int. J. Plast. (2014) , http://
dx.doi.org/10.1016/j.ijplas.2014.03.008 .
[167] J. Olbricht, A. Yawny, J.L. Pelegrina, G. Eggeler, et al. J. Alloys Compd. 579 (2013)
249–252.
[168] E. Prokoﬁev, J. Burow, J. Frenzel, et al. Mater. Sci. Forum 667–669 (2011) 1059–
1064.
[169] M. Peterlechner, T. Waitz, C. Gammer, T. Antretter, Int. J. Mater. Res. 6 (2011)
634–642.
[170] J. Burow, E. Prokoﬁev, C. Somsen, et al. Mater. Sci. Forum 584–586 (2008) 852–
857.
[171] Q.S. Mei, L. Zhang, K. Tsuchiya, et al. Scr. Mater. 63 (10) (2010) 977–980.
[172] H.P. Karnthaler, T. Waitz, C. Rentenberger, et al. Mater. Sci. Eng. A 387–389
(2004) 777–782.
[173] T. Waitz, Acta Mater. 53 (8) (2005) 2273–2283.
[174] T. Waitz, W. Pranger, T. Antretter, et al. Mater. Sci. Eng. A 481–482 (2008) 479–
483.
[175] T. Waitz, T. Antretter, F.D. Fischer, et al. J. Mech. Phys. Solids 55 (2) (2007) 419–
444.
[176] H.S. Liu, L. Mishnaevsky Jr., Comp. Mater. Sci. 76 (2013) 27–36.
[177] A.V. Idesman, V.I. Levitas, D.L. Preston, et al. J. Mech. Phys. Solids 53 (3) (2005)
495–523.
[178] V.I. Levitas, A.V. Idesman, G.B. Olson, Acta Mater. 47 (1) (1998) 219–233.
[179] A.V. Idesman, V.I. Levitas, E. Stein, Comput. Methods Appl. Mech. Eng. 173 (1–2)
(1999) 71–98.
[180] A.V. Idesman, V.I. Levitas, D.L. Preston, J.Y. Cho, J. Mech. Phys. Solids 53 (2005)
495–523.
[181] R. Kumazawa, F. Watari, N. Takashi, Y. Tanimura, M. Uo, Y. Totsuka, Biomaterials
23 (2002) 3757–3764.
[182] Y. Mine, S. Makihira, H. Nikawa, H. Murata, R. Hosokawa, A. Hiyama, S. Mimura, J.
Prosthodont. Res. 54 (2010) 1–6.
[183] X. Lu, X. Bao, Y. Huang, Y. Qu, H. Lu, Z. Lu, Biomaterials 30 (2009) 141–148.
[184] J.C. Wataha, N.L. O’Dell, B.B. Singh, M. Ghazi, G.M. Whitford, P.E. Lockwood, J.
Biomed. Mater. Res. B 58 (2001) 537–544.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 18

[185] M.F. Maitz, N.J. Shevchenko, J. Biomed. Mater. Res. A 76 (2006) 356–365.
[186] L. Tan, R.A. Dodd, W.C. Crone, Biomaterials 24 (2003) 3931–3939.
[187] J.M. Gil, J.A. Manero, J. Planell, F.J. Manero, J.A. Planell, J. Mater. Sci: Mater. Med. 7
(1996) 403–406.
[188] M. Assad, P. Jarzem, M.A. Leroux, C. Coillard, V.A. Chernyshov, C. Charette, C.H.
Rivard, J. Biomed. Mater. Res. B. 64B (2003) 107.
[189] L.I. Chu, C.Y. Chung, P.H. Lin, S.D. Wang, Mater. Sci. Eng. A 366 (2004) 114–119.
[190] I. Gotman, Adv. Biomater. 12 (7) (2010) B320–B325.
[191] G. Zorn, A. Lesman, I. Gotman, Oxide Surf. Coat. Technol. 201 (2005) 612–618.
[192] C. Leinenbach, D. Eiﬂer, Biomaterials 27 (2006) 1200–1208.
[193] D. Starosvetsky, I. Gotman, A. Shenhar, J. Mater. Sci.: Mater. Med. 12 (2001) 145–
150.
[194] D. Starosvetsky, I. Gotman, Biomaterials 22 (2001) 1853–1859.
[195] G. Meng, Y. Li, F.H. Wang, Electrochim. Acta 51 (2006) 4277–4284.
[196] F.L. Nie, S.G. Wang, Y.B. Wang, S.C. Wei, Y.F. Zheng, Dental Mater. 27 (2011) 677–
683.
[197] L. Liu, Y. Li, F. Wang, J. Mater. Sci. Technol. 26 (2010) 1–14.
[198] D. Cheng, V.L. Tellkamp, J. Lavernia, E.J. Lavernia, Ann. Biomed. Eng. 29 (2001)
803–809.
[199] H. Garbacz, M. Pisarek, K.J. Kurzydłowski, Biomol. Eng. 24 (2007) 559–563.
[200] B. Kasemo, J. Prosthetic Dentistry 49 (6) (1983) 832–837.
[201] J. Ryha¨nen, E. Niemi, W. Serlo, et al. J. Biomed. Mater. Res. 35 (1997) 451–457.
[202] J. Ryha¨nen, M. Kallioinen, J. Tuukkanen, et al. J. Biomed. Mater. Res. 41 (1998)
481–488.
[203] M. Assad, N. Lemieux, C.H. Rivard, L’.H. Yahia, Bio-Med. Mater. Eng. 9 (1) (1999)
1–12.
[204] R. Bhola, S.M. Bhola, B. Mishra, D.L. Olson, Trends Biomater. Artif. Organs 25 (1)
(2011) 34–46.
[205] D.J. Wever, A.G. Veldhuizen, J. de Vries, et al. Biomaterials 19 (7–9) (1998)
761–769.
[206] A.V. Yakubovich, G.B. Sushko, S. Schramm, A.V. Solov’yov, Molecular dynamics
simulation of self-diffusion process in titanium in bulk material, on grain
junctions and on surface, J. Phys. Chem. A (2014) (under review).
[207] E. Sikora, X.J. Wei, B.A. Shaw, Corrosion 60 (2004) 387–398.
[208] C.Y. Zheng, F.L. Nie, Y.F. Zheng, Y. b, S.C. Cheng, R.Z. Wei, Valiev, Appl. Surf. Sci.
257 (2011) 9086–9093.
[209] E.A. Levashov, M.I. Petrzhik, D.V. Shtansky, Ph.V. Kiryukhantsev-Korneev, A.N.
Sheveyko, R.Z. Valiev, D.V. Gunderov, S.D. Prokoshkin, A.V. Korotitskiy, A.Yu.
Smolin, Mater. Sci. Eng. A 570 (2013) 51–62.
[210] D.V. Shtansky, E.A. Levashov, I.V. Batenina, N.A. Gloushankova, N.Y. Anisimova,
M.V. Kiselevsky, I.V. Reshetov, RSC Adv. 3 (2013) 11107–11115.
[211] D.V. Shtansky, N.A. Glushankova, A.N. Sheveiko, M.A. Kharitonova, T.G. Moiz-
hess, O.V. Malochkin, E.A. Levashov, F. Rossi, Biomaterials 26 (2005) 2909–2924.[212] D.V. Shtansky, N.A. Gloushankova, I.A. Bashkova, M.I. Petrzhik, A.N. Sheveiko,
F.V. Kiryukhantsev-Korneev, E.A. Levashov, I.V. Reshetov, A.S. Grigoryan, Surf.
Coat. Technol. 201 (2006) 4111–4118.
[213] D.V. Shtansky, N.A. Glushankova, I.A. Bashkova, M.A. Kharitonova, T.G. Moizhess,
A.N. Sheveiko, F.V. Kiruhancev-Korneev, E.A. Levashov, M.I. Petrzhik, Biomater-
ials 27 (2006) 3519–3531.
[214] C. Auclair-Daigle, M.N. Bureau, J.G. Legoux, L.J. Yahia, J. Biomed. Mater. Res. A 73
(4) (2005) 398–408.
[215] Yu.P. Sharkeev, E.V. Legostaeva, Yu.A. Eroshenko, I.A. Khlusov, O.A. Kashin,
Compos. Interface 16 (2009) 535–546.
[216] L. Mishnaevsky Jr., D. Gross, Appl. Mech. Rev. 58 (5) (2005) 338–353.
[217] W.D. Nix, Met. Trans. A 20A (1989) 2217–2245.
[218] J.W. Hutchinson, Z. Suo, in: J.W. Hutchinson, T.Y. Wu (Eds.), Adv. Appl. Mech.,
vol. 28, 1991, pp. 63–189.
[219] A.G. Evans, J.W. Hutchinson, Acta Metall. Mater. 43 (1995) 2507.
[220] M.D. Thouless, Thin Solid Films 181 (1989) 397–406.
[221] M.D. Thouless, Annu. Rev. Mater. Sci. 25 (1995) 69–96.
[222] R.P. Vinci, J.J. Vlassak, Annu. Rev. Mater. Sci. 26 (1996) 431–462.
[223] S.G. Psakhie, A.Yu. Smolin, Yu.P. Stefanov, P.V. Makarov, M.A. Chertov, Tech.
Phys. Lett. 30 (2004) 712–714;
S.G. Psakhie, et al. Phys. Mesomech. 14 (5–6) (2011) 224–248.
[224] J.O. Galante, J. Lemons, M. Spector, P.D. Wilson Jr., T.M. Wright, J. Orthop. Res. 9
(1991) 760–775.
[225] U.W. Bischoff, M.A. Freeman, D. Smith, M.A. Tuke, P.J. Gregson, J. Bone Joint Surg.
76B (1994) 713–716.
[226] K. Hirakawa, T.W. Bauer, B.N. Stulberg, A.H. Wilde, M. Secic, J. Bone Joint Surg.
78A (1996) 1235–1243.
[227] M.J. Pappas, G. Markis, F.F. Buechel, Clin. Orthop. 317 (1995) 64–70.
[228] M.K. Harman, S.A. Banks, W.A. Hodge, J. Arthroplasty 12 (1997) 938–945.
[229] C. Liu, Q. Bi, A. Matthews, Surf. Coat. Technol. 163–164 (2003) 597–604.
[230] I. Gotman, E.Y. Gutmanas, G. Hunter, in: P. Ducheyne, K.E. Healy, D.W.
Hutmaher, D.W. Granger, C.J. Kirkpatrick (Eds.), Comprehensive Biomaterials,
vol. 1, Elsevier, Oxford, 2011, pp. 127–155 (Chapter 19).
[231] S.N. Massoud, J.B. Hunter, B.J. Holdsworth, W.A. Wallace, R. Juliusson, J. Bone
Joint Surg. Br. 79-B (1997) 603–608.
[232] A. Shenhar, I. Gotman, E.Y. Gutmanas, P. Ducheyne, Mater. Sci. Eng. A 268 (1999)
40–46.
[233] A. Shenhar, I. Gotman, S. Radin, P. Ducheyne, E.Y. Gutmanas, Surf. Coat. Technol.
126 (2000) 210–218.
[234] D. Starosvetsky, I. Gotman, Biomaterials 22 (13) (2001) 1853–1859.
[235] G. Sovak, A. Weiss, I. Gotman, J. Bone Joint Surg. Br. 82B (2000) 290–296.
[236] S.J. Wu, E.Y. Gutmanas, I. Gotman, Key Eng. Mater. 434–435 (2010) 481–484.L. Mishnaevsky Jr. et al. / Materials Science and Engineering R 81 (2014) 1–19 19

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